A serial number can be a crucial bit of information in determining the value of a shotgun. It's common for a shotgun to have a serial number but no information about the brand name of the weapon. Since an antique shotgun can be worth a lot of money -- ranging in value from hundreds to several thousands of dollars -- it's a good idea to use the serial number to obtain as much information about the gun as possible, including its year of manufacture and number of similar shotguns that were produced.
Use your computer to go to the manufacturer's website and see if they keep information about serial numbers. Remington, Browning and Mossberg, three of the world's largest shotgun manufacturers, provide online tools that will let you use your serial number to find out more details about your weapon.
Buy or borrow a copy of the Blue Book of Gun Values, published by Blue Book Publications, Inc. There are more than 1.3 million copies in print as of 2010. The Blue Book, which costs about £29, will include a range of potential serial numbers for each shotgun by manufacturer, including its current estimated value. If you know the brand of the shotgun, you can find the model easily. If you don't, the book includes photos of shotguns. Use them to identify your model, then confirm with the serial numbers cited in the book.
Find an appraiser with experience in determining the value of shotguns. Ask someone at your local gun store for ideas, search online or ask at a local gun show for an appraiser's name if you can't find one on your own. A good shotgun appraiser will have a wealth of experience and should be able to offer you some good guesses about your model of shotgun, which you can then confirm online or with the Blue Book.