Would such tags work for this application?
No. Active tags are fairly large, as they have a battery and a printed circuit board. While they have been getting smaller, they are still too bulky and expensive for tracking large numbers of jewelry items (they would work fine on larger containers carrying trays of jewelry, however). Plus, you would not necessarily need to read the tag on a ring from 100 feet away. It is often better to have a reader under a shelf interrogating the tags, so that you would know a particular item was in its rightful place or had been removed from a specific shelf. Typically, small passive tags are used for monitoring jewelry.
—Mark Roberti, Founder and Editor, RFID Journal