Originally, I thought maybe I could find adhesive foil (like the copper foil used for doing stained glass), and do something with that and my soldering iron. But after a bit of looking around on the internet, I realized that making a metal setting for jewelry requires actual, you know, metal smithing, something I wasn't prepared to do. I did, however, find some pendants created with a technique called "wire wrapping." I thought they looked pretty, and it didn't look too difficult, so I thought I'd give it a try. One roll of silver wire later (cost: under $5), about half an hour of labor, (guided loosely by the instructions on this website), and I have this:
Here's the ammonite before being wrapped (along with some chain stuff I later decided not to use):
It was really, really simple to do, and I'm very happy with the results, especially for a first effort. I think with a little bit of practice, I could make things with this technique that would look much more professional. In fact, I'll probably do some of that. (Hah. Some of you may be getting jewelry this year for the holidays :D).
Here's another view of the necklace:
And here's me wearing it, so you can see the size of the finished piece: