Purely out of curiosity, I have to ask - why did you ask for the rings back? You gave them to her when you got married. Did you have a wedding ring? Did she ask for it back? And why would you want these reminders sitting wherever they are sitting?
Background - ExDH did not ask for my rings back, I did not ask for his back, and the mediator never suggested it, the rings never came up in all our long tedious financial mediation. They only showed up as part of my overall jewellery valuation, which was part of the total assets valuation for each of us, and the jeweler valued them at the price of gold plus a small amount for the diamond. Now they are sitting in a drawer while I decide what to do with them. Best idea so far, from the appraiser, take the diamond and mount it in a necklace I have. I will certainly never wear them again as rings.
And if you find a really good place to sell them, let me know ;-) I am still in debt from the divorce, a little extra money wouldn't hurt.