Hmmm that is a tough one. But if you feel you have made all of the effort to find the owner that you could, you cannot possibly make it your life's mission to hold on to it forever to find the owner. What, should you notify the police and let them take it, bag it and put in in a basement where someone else will steal it? Maybe I watch too much TV. I think you should take it to a jeweler and find out what it is worth before you start worrying.