Self-examination or prove (KJV) is related to the Greek word dokimazo.

It means to test, examine, and scrutinize to recognize as genuine and deemed worthy.

Dokimazo is used in the NT in various contexts. 

Inward (self) Proving

 1. 2Co13:5, self-examination focuses on examining whether one is in faith, living by the power of God as displayed in the resurrection of Christ (2Co13:4).

This faith of 2Co13:5 is the belief in the hope of this resurrection, our resurrection, especially the 1st resurrection of Rev20:6 that needs to be earned according to Paul in Phil3:10-11.

Paul goes on to frame this faith in the resurrection as the truth in 2Co13:8.

The other inward proving is related to taking the holy communion found in 1Co11:28.

Outward Proving

2. The other forms of examining in the NT are no longer, about an inward examination but an outward examination

2.1 Rom12:2,  Rom2:18, andv 1Th5:21- Prove what is good to discover and align with God’s will.

2.2 2Co8:8 and Phil1:10 are about proving love and excellence for sincerity, Gal6:4 proving one’s own work (of bearing burdens to fulfill the Law of Christ), 1Jhn4:1 is about proving every spirit relating to false prophets.

In-Summary

Personally, I practice self-examination using a clear and pure conscience to guide me in areas of sincerity, bearing the burdens of Gal6:2 and testing and validating God’s will.

I talk, think and dream about the resurrection daily, so the encouragement to examine one’s faith in the resurrection is moot for me but needful for the body of Christ.

Other forms of self-examination or examinations would be outside the wise counsel of the NT scriptures.