Sorry for the hijacking...Here's an attempt to address the OP:
1. It seems that there are scriptures in which some people can believe themselves to be saved, but not be. (those who will cry "Lord, Lord," to Jesus, but he will say "I never knew you."...or the Jews paul prays for in romans 10:1-3, who had a zeal for God, but because they would not accept God's righteousness, and tried to establish their own, pauls says he is praying for their salvation.)
2. It also seems that there are places in scripture that God hardens people into their chosen path of rebellion:
-2Th 2:11 For this reason God will send upon them a deluding influence so that they will believe what is false,
2Th 2:12 in order that they all may be judged who did not believe the truth, but took pleasure in wickedness. (NASB)
-Pharoah,
-Romans 1: God "gave them over" to their sinful desires.
3. The question is, is it unreasonable, or unbiblical to think there is N

VERLAP between these two groups of people: Those who mistakenly believe they are saved, and those who God has "hardened, given over, or deluded"? I don't think it is unreasonable to believe there is some overlap.
4. Regarding your last question, a calvinists knows he is one of the elect just like anybody else knows: By examining himself ACCORDING TO THE SCRIPTURES that warn us in certain ways:
-1 Cor. 16:22 - Do I Love the Lord?
-Rom. 10:1-4 - Is my passion for the Lord based on true knowledge, that is, Am I attempting to trust in my own righteousness, or that of Christ?
-1 John - Does my life reflect love for God and neighbor, and a desire to obey God's commands?
5. If I were one of those deluded into thinking I was saved when I was not, then I would not be willing to submit myself to these, and other, scriptural tests by which we are told to examine ourselves.