The next time you run into this person, remind her about the coin and tell her that you lost it and can't find it anywhere and how much it meant to you and that you now feel terrible for losing it. Watch her reaction.
Bonus points if you mention that you wanted to give her the coin as a present.
If that doesn't help, set her up by leaving another valuable object out. While you step out of the room for a bit, turn on a video camera.
