Calvinist blogger C Michael Patton from Credo House writes (Link):
It may surprise you to know that just about every contact I have had with people who are doubting their salvation are Calvinistic in their theology. In other words, they believe in unconditional election. These are the ones who believe in perseverance of the saints. These are the ones that believe that we cannot lose our salvation! Yet these are the ones who are doubting their faith the most.
Their issue has to do with their election. Are they truly among the elect? If they are, they believe their faith will persevere until the end. But if they are not, there is no hope. But how are they to know for sure whether they are elect? Maybe their faith is a stated faith? Maybe it is false. The gentleman I talked to today was so riddled with doubt, he was having thoughts of suicide. “How do I know my faith is an elect faith?” He wanted assurance so badly, but felt that his Calvinistic theology prevented him from ever having such assurance.
Influential Calvinist John Piper similarly has said (Link, quote is in the audio only at 45:20):
I deal with this as much as anything, probably, in the people that I’m preaching to. Fears, and doubts, doubts not about objective “Did He rise from the dead?” – very few people are wrestling with that – but “Am I in? Am I saved?” That’s very common for people to wrestle with. 
Though I hold, with Calvinists, that all true believers will persevere, in this post I want to highlight the distinction between my view and theirs: that in Calvinism, ultimately, there is no assurance that you are one of the elect, and therefore no assurance that you are right with God.
Why? Because in Calvinism assurance is not grounded in the promises of God (His promise to save all those who repent and believe on the basis of Jesus’ perfect life, substitutionary death and His resurrection), but rather in God’s “secret decree” to elect “whosoever He wills”. As I’ve discussed before, Calvinism makes God fundamentally untrustworthy (Link and Link). The Calvinist view (at least as held by Edwards/Piper) is that God will always do whatever brings Him the utmost glory, whether that means decreeing your forgiveness or your damnation in eternal torment (addressing this false idea that God can be more glorified through unconditional damnation than through sinners turning to him in repentance and faith will have to wait until another post).
Here’s the worst part: in Calvinism, not even your own conscience that you are right with God is enough to provide you with assurance (contra. Romans 8:16). Calvin himself held that God might provide you with what he called, “evanescent grace”; that is, false assurance so that you will be damned more severely. He wrote (underline mine):
...experience shows that the reprobate are sometimes affected in a way so similar to the elect, that even in their own judgment there is no difference between them. Hence it is not strange, that by the Apostle a taste of heavenly gifts, and by Christ himself a temporary faith, is ascribed to them. Not that they truly perceive the power of spiritual grace and the sure light of faith; but the Lord, the better to convict them, and leave them without excuse, instills into their minds such a sense of his goodness as can be felt without the Spirit of adoption. Should it be objected, that believers have no stronger testimony to assure them of their adoption, I answer, that though there is a great resemblance and affinity between the elect of God and those who are impressed for a time with a fading faith, yet the elect alone have that full assurance which is extolled by Paul, and by which they are enabled to cry, Abba, Father. Therefore, as God regenerates the elect only for ever by incorruptible seed, as the seed of life once sown in their hearts never perishes, so he effectually seals in them the grace of his adoption, that it may be sure and steadfast. But in this there is nothing to prevent an inferior operation of the Spirit from taking its course in the reprobate. Meanwhile, believers are taught to examine themselves carefully and humbly, lest carnal security creep in and take the place of assurance of faith. We may add, that the reprobate never have any other than a confused sense of grace, laying hold of the shadow rather than the substance, because the Spirit properly seals the forgiveness of sins in the elect only, applying it by special faith to their use. Still it is correctly said, that the reprobate believe God to be propitious to them, inasmuch as they accept the gift of reconciliation, though confusedly and without due discernment; not that they are partakers of the same faith or regeneration with the children of God; but because, under a covering of hypocrisy, they seem to have a principle of faith in common with them. Nor do I even deny that God illumines their minds to this extent, that they recognize his grace; but that conviction he distinguishes from the peculiar testimony which he gives to his elect in this respect, that the reprobate never attain to the full result or to fruition. When he shows himself propitious to them, it is not as if he had truly rescued them from death, and taken them under his protection. He only gives them a manifestation of his present mercy. In the elect alone he implants the living root of faith, so that they persevere even to the end. Thus we dispose of the objection, that if God truly displays his grace, it must endure for ever. There is nothing inconsistent in this with the fact of his enlightening some with a present sense of grace, which afterwards proves evanescent. (3.2.11, Institutes of Christian Religion, Link)
Later he writes again (underline mine):
Besides this [the universal call] there is a special call which, for the most part, God bestows on believers only, when by the internal illumination of the Spirit he causes the word preached to take deep root in their hearts. Sometimes, however, he communicates it also to those whom he enlightens only for a time, and whom afterwards, in just punishment for their ingratitude, he abandons and smites with greater blindness. (3.24.8, Institutes of Christian Religion, Link)
Calvinist AW Pink wrote along these same lines, claiming that there are people who have “a faith in Christ which does not save...those who believed in, rested upon, leaned upon, relied upon the Lord, but who were, never the less unsaved souls...”, and again “...Scripture also teaches that people may possess a faith which is one of the Holy Spirit, and yet which is a non-saving one” (Studies on Saving Faith, Part II(1), Link).
Even C Michael Patton, in the article linked above, states “I could have a false faith, but I don’t believe I do. This ninety percent assurance will have to do. The witness of the Spirit I have today is enough for today.”
I hope these quotes are as stunning to you as they are to me. And I hope you can see from them what a distorted view Calvinism has of the character of God. In this view (where God provides false assurance to unbelievers), God seems more like the false prophets and false christs who lead many astray (Matthew 24:11) than like Jesus as He is shown throughout the Gospel accounts. Both Calvin and Pink use Hebrews 6:4-6 to support this false faith from the Holy Spirit. While most Calvinists I know would not call it “evanescent grace”, they do hold to some form of it; the alternative is to agree with the Arminian that grace is resistible. In other words, if you believe in irresistible grace, then the only explanation for someone moving towards God but not believing is that God provided grace, but not enough for that individual to believe and be saved. Arminians, on the other hand, are able to avoid this dilemma by holding that grace is resistible: Arminians affirm that the grace to believe is from the Holy Spirit, but it is man’s fault, not God’s, if we refuse to be saved.
Where is the Christian’s assurance grounded?
Biblical assurance comes from the promises of God, and so the question boils down to this: Do you believe that God will do what He has promised? The Calvinist can possess no such assurance, since their doctrine holds that God can say one thing while decreeing something completely contrary (for example, consider their view of passages like Ezekiel 33:11, or 1 Timothy 2:4). Even the inward witness of the Spirit is not enough to provide assurance since, as shown above, false assurance is also said to have come from the Holy Spirit.
In contrast to the Calvinist position, I believe Steve Horn has expressed the Biblical view precisely, in his article on the Traditional Statement, when he writes (bold mine):
It appears that the only sure foundation for assurance is the Traditionalist view that assurance is based on the accomplishments of Christ and His promises to anyone who believes by faith. How does one know he is saved? He believes that Jesus is who He says He is and that He will do what He says He will do. Feelings can certainly support such assurance, but there will be days when such feelings are not present. Works support such assurance but there will be days when such works are not present. If the inner sense of the Spirit’s presence and the outward working of the Spirit are never on display, then soul-searching as to one’s salvation is indeed necessary, but the basis of the search is still the same. The question is not, “Do my affections substantiate my election?” or “Have I done enough?” but “Have I trusted in Christ alone for salvation?” Assurance is not rooted in the doctrine of election or the doctrine of sanctification. It must be rooted in the doctrine of justification, or perseverance becomes a cause of doubt not a source of assurance. Calvinism tends to include inner witness and outward works as part of the basis for assurance because of the demands of determinism. The Traditional view, because it has a different view of freedom, allows assurance to rest on the only suitable cornerstone: justification by faith. (Commentary on Article 9: The Security of the Believer, Link)
Arminius himself put it similarly (HT: JeremyO), "the foundation of the certainty of salvation [...] is dependent upon this decree, 'they who believe, shall be saved:' I believe, therefore, I shall be saved" (Link). And:
Since God promises eternal life to all who believe in Christ, it is impossible for him who believes, and who knows that he believes, to doubt of his own salvation, unless he doubts of this willingness of God [to perform his promise.] But God does not require him to be better assured of his individual salvation as a duty which must be performed to himself or to Christ; but it is a consequence of that promise, by which God engages to bestow eternal life on him who believes. (Link)
Grounding the promises of God, we have the impeccable character of God. As the blogger from Arminian Perspectives put it, “in knowing that God desires his salvation and will give him all the power he needs to continue to trust in Him, the Arminian has a strong basis for assurance in final salvation...” (Link). The firm foundation of our faith is the assurance that “God is altogether worthy of our trust”, wrote AW Tozer (Link):
The character of God is the Christian’s final ground of assurance and the solution of many, if not most, of his practical religious problems. Some persons, for instance, believe that God answered prayer in Bible times but will not do so today, and others hold that the miracles of olden days can never be repeated. To believe so is to deny or at least to ignore everything God has revealed about Himself.
We must remember that God always acts like Himself. He has never at any time anywhere in the vast universe acted otherwise than in character with His infinite perfections.
What does God promise?
When Paul dealt with the accusation that God may be unfaithful to his promises, he answered unequivocally, “By no means! Let God be true though every one were a liar”. (Romans 3:4 ESV).
When it comes to who will be saved, the Bible is equally clear (quotations from the NIVUK):
- Do you believe in the name of Jesus?
- John 1:12-13. “Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God – children born not of natural descent, nor of human decision or a husband’s will, but born of God.”
- John 3:14-18, Jesus said, “'Just as Moses lifted up the snake in the wilderness, so the Son of Man must be lifted up, that everyone who believes may have eternal life in him.' For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son.”
- John 3:36, “Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on them.”
- John 5:24, Jesus said, “Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life.
- Acts 10:43, “All the prophets testify about him that everyone who believes in him receives forgiveness of sins through his name.”
- Acts 16:30-31, “He then brought them out and asked, ‘Sirs, what must I do to be saved?’ They replied, ‘Believe in the Lord Jesus, and you will be saved – you and your household.’”
- Romans 10:9-10 & 13, “If you declare with your mouth, ‘Jesus is Lord,’ and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved...for, ‘Everyone who calls on the name of the Lord will be saved.’”
John said he wrote his first epistle, “to you who believe in the name of the Son of God so that you may know that you have eternal life” (1 John 5:13). Do you believe? Then what is God’s promise?
The apostle Paul wrote, “That is why I am suffering as I am. Yet this is no cause for shame, because I know whom I have believed, and am convinced that he is able to guard what I have entrusted to him until that day.” (2 Timothy 1:12)
Jesus said to Martha:
I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this? (John 11:25-27, underline mine)
Calvinists are fond of quoting Isaiah 46:
I say, “My purpose will stand, and I will do all that I please.” From the east I summon a bird of prey; from a far-off land, a man to fulfil my purpose. What I have said, that I will bring about; what I have planned, that I will do. Listen to me, you stubborn-hearted, you who are now far from my righteousness. I am bringing my righteousness near, it is not far away; and my salvation will not be delayed. I will grant salvation to Zion, my splendour to Israel.
Do you think this applies to everything except God’s promise to save everyone who believes? “The one who calls you is faithful, and he will do it.” (1 Thessalonians 5:24)
 At another time, when answering a question about why Christians are not made perfect the moment we believe, Piper said:
I know people, and I would say this about myself, for whom the greatest threat to my perseverance and my ultimate salvation is the slowness of my sanctification. It’s not theoretical issues like "Did He rise from the dead?" or the problem of evil. I’ve got answers. But why I sin against my wife the same at age 62 that I did at age 42 causes me sometimes to doubt my salvation or the power of the Holy Spirit, or, you get the idea. This question is not theoretical.” (Link, quote is in the audio only at 36:03)
 Before this comment he rightly states:
You ask me: Michael, do you know you are saved? My answer: yes. You ask me: Michael, do you have assurance? My answer: yes. You ask me: Michael, why do you believe you are saved? My answer: because today I am still believing.
- Andrew Dragos, “John Wesley on Assurance: Can You Know You’re Saved";
- Brian Abasciano, "Security in Christ" in “The FACTS of Salvation: A Summary of Arminian Theology/the Biblical Doctrines of Grace";
- Imperfect Reflections, "Why I Care About Calvinism";
- Arminian Perspectives, “An Important Admission on Salvation Assurance from Prominent Calvinist C Michael Patton";
- James M Leonard, “Assurance of Salvation in Calvinism?";
- William Birch, "Arminius vs Calvin on Assurance of Salvation and Perseverance".
On Evanescent Grace:
- Examining Calvinism, "Evanescent Grace";
- Ron F Hale (SBC Today), "Calvin's 'Temporary Faith' for the Reprobate".