Hey, just caught up with this thread. Great topic!
I just bought my wife a 1.5 karot diamond ring recently, so this topic "hits home". We paid nearly $20k for it. It was a super specific grade or color or something, + custom made by a designer, so there was cost for that as well. Anyhow, I was surprised when.... we were looking at various stones, when the jeweler showed us the micro-laser mark thing in there (telling country of origin, for instance). It could only been seen under high power magnification, and you had to know where to look. This is a fairly recent technology, and can also be made to inscribe serial #s too, as I understand it.
I've been in this hobby long enough (30 yrs.) to remember a time when this was the stuff of science fiction! The only rings we ever thought we could find the owner of, was class rings (by virtue of initials, school, etc...). All else was OURS, and there was no "feeling bad" about it. (Afterall, that's why we got into the hobby, right

)
Aside from laser inscriptions on diamonds, I did hear that insurance companies, when insuring very valuable rings, would put an inscription in the
band of the ring. This was years ago, before the laser inscription technology on diamonds I guess. I heard that if you found such a ring with a serial # (plainly visible inside the band), that insurance companies do pay a reward for their return, since they want to recoup from their losses from possibly having paid out to their insured. But now it's gone beyond that, to where a lot more rings, besides obviously engraved ones, can potentially be traced. Strange!
Although I've heard that insurance companies will pay a reward to get their insureds property back from a finder, it presents a big problem: That may only been when it's been admitted "lost" by the owner. You know, like "I lost it on the beach while I was throwing a frisbee" etc... But if you think of it, MOST people don't know when they've lost their ring, barring someone who felt it fling off their hand, etc... How many times have you heard of this scenario: A lady goes to the ladies room, and goes to wash her hands. She accidentally leaves the ring on the sink, and walks off without it. She comes back a minute later, and it's too late! It's gone

She reports it "stolen", right? Now think of it: what if she'd actually lost it on the beach 30 minutes before, but only *thinks* she left it in the ladies room? Or how about: a lady puts her ring on a picnic table, with her other beach towel and stuff, for safekeeping, while she swims. The table gets bumped, the ring falls down to the grass or sand below. When the lady gets back, she thinks "It's stolen!".
I have hunted for many gold rings, at the behest of owners, who are sometimes not sure where it is. They only know that at the end of the day, they noticed it was gone. A lot of them may report "stolen", since they may genuinely think so, or are guessing it was, etc.... The point is, whereas YOU AND I may look at our finds as "lost", they may be in the police sytem as "stolen" at a larger percent of the time that we think.
My friend once found a high school class ring at a school yard. He was easily able to trace the ring, since his daughter went to that school, and they had a school year book right there. My friend called that family, got a voice-mail machine, and said something to effect of "hey, I found your ring today. If you want it back, call me to discuss it" (don't remember the exact wording). That night, there was a knock at his door, and it was the POLICE! Seems he was under investigation for extortion, since, it turns out, the ring had been reported stolen. The ring was taken from him, and he never got so much as a thankyou

He said that from then on, he was never going to track down owners again (he may have said that half-jokingly, but I can see how some people would mean it sincerely). That was at a time when you could go to the smelt place, and those guys never cared about the initials and school, etc.. But in this day & age of laser inscribed stones, there may be no getting around it. Wierd!
I guess I'd take my chances with trying to trace it, seeing if there's an insurers reward, or owners greatful-heart reward. Not that I need the money, but I do enjoy the extra spending cash, and ....... over the years.... have sold off most of my jewelry. Unless the ring fit my wife, why would I have any need for it anyhow? Other than looking nice in a display case, it doesn't do us finders any good. So I'm one of those people who keeps very little of what he finds, and liquidates the rest from time to time.
Interesting topic! Guess I'll have to think about this more, next time I personally find a larger inscribed diamond. Have never found one larger than 1/3 karot, so it's never been an issue for me, thus far.