I say just keep it, put it away somewhere and take it out again a really long time from now to see how you feel. Most likely you will feel different. I actually have a box with pictures, letters, movie tickets(cheesy i know) of an ex bf. We didn't go out for long but i did know him since the 2nd grade and we were each other's first crushes, then we dated officially in 10th grade. Anyway he sent me lots of letters when i was at camp one summer and i kept them and pictures of him. When we broke up i was thinking of throwing it all out but instead i put it away in my closet, now when i take it out i just laugh about it. It doesn't make me sad or anything, but i like to go back and read the letters. And maybe someday i can show my kids, cause they are memories after all and part of my history
Even if he wasn't even a serious bf, hes the only bf that actually wrote me letters, and i think thats cool since we have all this technology now. Anyway if you really dont want it sell it, and take it to a jewelery shop to see how much its worth.