One of the main points of Calvinistic theology is their doctrine of the perseverance of the saints. This is the doctrine in which one who is elect of God cannot lose his or her salvation.1
"In like manner, in the Gospel of Luke, those in whom the seed of the word is choked before it brings forth fruit, or in whom, from having no depth of earth, it soon withereth away, are said to believe for a time. Such, we doubt not, eagerly receive the word with a kind of relish, and have some feeling of its divine power, so as not only to impose upon men by a false semblance of faith, but even to impose upon themselves. They imagine that the reverence which they give to the word is genuine piety, because they have no idea of any impiety but that which consists in open and avowed contempt. But whatever that assent may be, it by no means penetrates to the heart, so as to have a fixed seat there. Although it sometimes seems to have planted its roots, these have no life in them. The human heart has so many recesses for vanity, so many lurking places for falsehood, is so shrouded by fraud and hypocrisy, that it often deceives itself."2
This being the case, I think it's important to point out the true lack off assurance any Calvinist truly has. If anyone can be fooled about their conversion, no Calvinist can say they ARE elect with certainty. They feel elect, maybe, but they have no idea if Christ died for them or not, since Christ only died for a select few. The irony is most Calvinists tout this as one of their distinctive advantages, they KNOW they are saved; but we can see there is really no grounds for this assurance because they can't be sure their Christian experience isn't the false assurance Calvin described.
R.C. Sproul writes:
"A while back I had one of those moments of acute self-awareness…and suddenly the question hit me, 'R.C., what if you are not one of the redeemed? What if your destiny is not heaven after all, but hell?' Let me tell you that I was flooded in my body with a chill that went from my head to the bottom of my spine. I was terrified… I began to take stock of my life, and I looked at my performance...”3Am I missing something? What good would introspection do in this case? If you aren't elect, no amount of introspection is going to change that!!! The introspection does nothing in any case. If upon introspection you find you aren't elect, there's nothing you can do to change that.
As an Arminian, however, there is good grounds for assurance. We know that Christ has died for all (1 John 2:2, 2 Peter 3:9, etc.) and by faith we can have the righteousness of Christ imputed to us (Acts 16:31, Romans 3:28, Ephesians 2:8-9). We also know no believer can be separated from the Lord (Romans 8:35-39).4
1 There are some Arminians and other non-Calvinists who hold to this theological distinctive. The reasoning, however, is different in the non-Calvinist versions. While in Calvinism it is necessary when considering unconditional election and limited atonement, in non-Calvinist theology it is seen as simply a promise of God that once a person is saved they cannot lose their salvation.
2 John Calvin, Institutes Book 3 Section 2, http://www.reformed.org/master/index.html?mainframe=/books/institutes/
3 R.C. Sproul, “Assurance of Salvation,” Tabletalk, Ligonier Ministries, Inc., 1989, 20. Cited in Dave Hunt, What Love is This
4 However, I do believe one can cease believing and, therefore, is no longer in Christ.