We often get request for items our clients believe to be "Solid" or "Sterling Silver", but like this early 20th Century trinket box pictured above are not. Generally a lacking of any markings on a piece like this one is a good indicator it's very unlikely to contain any silver at all other than a thin plating. Pieces like this Trinket box generally date from the first quarter of the 20th Century and were made of a base metal such as Spelter or Britannia metal, the surface with the barest of silver plating. Some will have company markings, but no indicator of the metal it's constructed of.
By International conventions anything constructed of silver is generally well marked to indicate its silver content. Such markings are often called "Hallmarks" after the British system of marking with a series of stamps that indicate the date, maker and silver content. Other markings can include numerical markings such as "925' ( for Sterling-92.5% pure silver), "800" ( for 80% pure silver), or the word "Sterling". Unmarked pieces can be tested for silver content, most Jewelers and Coin Shops can provide this service for a small fee.
Originally boxes like this one would have had a paper or foil label indicating its country of origin and possibly the maker/importer of the piece, but these are often removed after sale or have simply fallen off over time. Values for these silver plated trinket boxes are very modest, with most selling at auction for less than $50.00 in most cases.