This is an educated guess --
Since it is thimble shaped, it may well be a thimble holder. Other
things that could be in this shape are a vinaigrette (for holding
smelling salts) or a seal holder. In the late 19th and early 20th
century items such as this would be suspended from a chatelaine that
was pinned to a woman's skirt or dress at the waist. Even at a
later time a seamstress might find it handy to wear her thimble by
pinning it to her clothing.
You might want to take your little box to F. B. Hubley Auctioneers,
364 Broadway, Cambridge, MA. Also, Karin Phillips may still have a
shop on Broadway a few doors down (toward Prospect St.) from
Hubley's. Karin is very knowedgeable about objects like this.
Another place where you might get help with identification is
Marika's Antiques 130 Charles St. in Boston or at one of the other
antiques dealers on that street.
Plum Blossom Antiques & Jewelry
Fall River, MA