3 And not only that, but we also glory in tribulations, knowing that tribulation produces perseverance; 4 and perseverance, character; and character, hope. 5 Now hope does not disappoint, because the love of God has been poured out in our hearts by the Holy Spirit who was given to us.
Romans 5:3-5
In this world you will have trouble.
John 16:33
There are none of us who haven’t some backstory of trouble. Paul spends most of the first part of Romans up until Chapter 5:2 thrashing out the wonders of being saved by grace not works. Then he suddenly changes the subject to troubles. Grace is still in play at this point. Paul is pointing out that when we go through troubles, because of grace, we glory in them. This is something that is possible for those who have privileged access to grace (v.2). We can also call on grace to persevere through troubles.
Anyone who has continued to believe and stand firm in faith by the grace of God through all sorts of trials then receives a certificate. The word often translated “proven character” in the English is the Greek word “δοκιμὴ” (doki-may). It sounds like our English word “document”.
There is a book I use to keep me correct when studying the Greek: Exegetical Guide to the Greek New Testament: Romans Copyright © 2017 by John D. Harvey. It says this about that word:
Δοκιμή, -ῆς, ἡ describes the result of going through a test (…. cf. 2 Cor 2:19; 8:2; 13:3; Phil 2:22); NEB translates it as “proof that we have stood the test.”
After you go through a test and prove God’s grace in you by staying faithful to Him through it, then you get a cert. It’s not a physical document but, like a cert you might get at university or college, it is a record of having achieved something.
People who have suffered for a long time and stayed faithful have an authority and peace (cf. Hebrews 12:11) that can be recognised by others. It is part of the name God gives them that others can see (Rev. 3:12).
The more tests passed the more cert(aintie)s we get. We experience the love of God poured out in our hearts in greater measure with each passed test. Our hope in Him is not disappointed if we persevere in trial (cf. James 1:2-4).