Swiss music boxes began to be made at the end of the 18th Century, with the first noted maker being a clockmaker named Antoine Favre from Geneva. Music boxes soon became popular in both Europe and America throughout the 19th Century and into the beginning of the 20th Century before they were gradually replaced by phonograph, gramophone and more modern music players. Today, they are generally seen as decoration, conversation pieces or children's toys, although new luxury examples are available, some of which even sell for thousands of dollars.
Find the maker's name. A good-quality antique music box should bear a maker's mark either on the inside or bottom of the box or, more likely, on the mechanism itself. This ought to give some idea of when the box was made, because most Swiss music box makers went out of business many years ago. Once you have the maker's name, try to find out the history of the company through a search on the Internet. You may even be lucky enough to find a serial number you can cross-reference, or even a date of manufacture.
Examine the box and mechanism. Look to see how the box is decorated. If it is in Art Deco style, for example, then it is likely to have been built in the 1920s or 1930s. If it has romantic pastoral scenes, it could come from the 19th Century. Match wood and finishes to prevailing styles of furniture at the time, especially in Switzerland. Take into account the materials used: If the box is made of plastic or the mechanism of aluminium, it was not made in 1840. The mechanism could give a more exact idea. If it has exchangeable music cylinders, then it was certainly built later than 1870, because this was when this system was invented. Exchangeable disk models were introduced around a decade later. Compare the mechanism to online pictures of music box mechanisms from different eras in order to get a match.
Find out the history of your music box. If possible, try to find out the history of the music box's previous owners. The trail may lead you back to the person who originally bought it new.
Research antiques catalogues. This may take some time and effort, but it may be the best way to date your box. Look for listings of other boxes made by the same maker. Many antiques dealers have online catalogues that may make the search easier. Try the "Antiques Trade Gazette" to get you started.
Take your box to be assessed by a specialised auction house in your area (auction houses are preferable to dealers who may try to charge you for the service). Because Swiss music boxes are very collectable, an auction house should have an expert willing and able to help.