*In a medieval context* I not only agree with Anne that girdle would probably be entirely correct, I would even wonder whether belt might very likely be wrong, depending on the piece's function. Is the picture at the link above perchance similar to the kind of object you're describing? If so, the Metropolitan Museum certainly ought to know what it's called.
I'm no expert, so I will gladly defer to any that may later show up. But just off the top of my head, I would say that a girdle was normally a narrower, lighter, cord-like item, often of metal, worn over a woman's gown or a man's tunic, primarily for decoration, partly as a piece of jewelry, often with one or both ends dangling, and partly to give shape (i.e. a waistline, often dropped) to a otherwise loose garment.
In contrast, a belt tended to be wider, heavier, and more functional, often of leather, worn primarily by men, and serving to hold up trousers and/or to hold a sword, purse, etc.
A web search for images of both, plus the word 'medi(a)eval' (or Byzantine or Greek or Roman or whatever), might be helpful.
In any case, surely it's safe to say that if you're already talking about medieval (or earlier) clothing and jewelry, no one is going to picture a 1950s-era elastic undergarment. However, if it would make you feel better, you could always try working in both words, e.g., 'a cotton tunic belted with a girdle made of coins.' (-: