The shop I went to is called Vaggi. Besides the Buccellati franchise, they also have the Roberto Coin franchise as well as their own designs. What I would look for are antique Florentine jewellery. They're very intricate and some have the Buccellati type of toolwork. I only shopped at Vaggi so I'm afraid I can't recommend you another shop. But there was another shop I found, thanks to the guide book, that has been making jewellery for 5 centuries! Imagine that! It's at 10R Piazza Del Duomo (just next to the Duomo), and the shop is called Torrini. I didn't quite like the designs though.
You sure you can't stow away in your parent's luggage? If you love jewellery, Florence is heaven! It is, after all, a town of artisans.
OMG - Vaggi is our good family friend. My parents literally changed my diaper 26 years ago on his counter while I played with the chains. That is SOO funny. We are going to visit in 3 weeks and have plans to see him and his wife. That is hysterical!