Can a person be saved, but not be absolutely certain about it? This question rightly deals with the difference between assurance and security. I’d agree with those who say that assurance is the subjective side of the issue and security (or eternal security) is the objective side of the issue. That’s to say that assurance 
has to do with how one feels and is related to sense experience regarding salvation while the issue of security relates to the biblical fact or truth or reality concerning the issue.
We learn that obedience to God’s instructions in our day to day lives is one way to build assurance into our lives. The New Testament assures us of this truth, but it also reminds me that sometimes “our conscience condemns us” (1 John 3:20) when God does not. There seems to be times when a person can be truly secure but not feel that way. I remember the illustration that was used about the two passengers on a plane. One was comfortable and relaxed and read a novel and enjoyed his meal. He was comfortable and confident that he’d get to where he was going. The other gripped the arm rest with all his might, sweated, imagined terrible crashes and just worried about a safe arrival. The plane landed as scheduled. The first passenger was secure and assured. The second was just as secure but had no assurance, yet he too arrived safely at the destination. The security on the flight did not have anything to do with how the individuals felt toward it. It was solely dependent upon the worthiness of the vessel and those in charge of it just as our salvation is. Yet a person may be on the plane, (believe that Jesus died for them), and because of the weakness of our flesh still not feel like it all the time.
The New Testament is clear about God’s desire for all His believing children to not only have the security of their eternal destiny established firmly in their minds, but to live each day with that sense of deep assurance that should come from that doctrine. The writer to the Hebrews says, “And we desire each one of you to show the same earnestness in realizing the full assurance of hope unto the end.”
Chuck
“Let us draw near with a true heart in full assurance of faith … Let us hold fast the confession of our hope without wavering for he who promised is faithful.” Hebrews 10:22-23