Go to Antique Guns at the related link and describe your firearm in as much detail as possible (and in the correct category or a couple of them will give you a hard time). The people there will give you an estimate of the value and help you determine if you really need a professional appraisal, and if so, guide you in the right direction.
There are several specialized auctions houses in the U.K. (and the U.S.) and other general auctioneers like Christie's and Sotheby's who have specialized arms auctions from time to time. They will freely advise you as to what you might expect if you put your item up for sale. Fees can be high, however. You might also try one of the U.K.'s best antiques arms dealers, Peter Finer, who I can wholly recommend as being fair in his dealings. However, he only buys and stocks the finest examples.
Contact the National Rifle Association, and ask for a referral to a member dealer in that area.
You will need the services of a professional appraiser familiar with antique firearms.
Take it to a firearms dealer or appraiser. There are also plenty of books on antique firearms at your local library.
go to http://gunbroker.com/
you can get it from an appraiser or at some antique roadshows.
Library, internet, Standard Catalog of Firearms.
To find information about a single shotgun made by W.H. Davenport Fire Arms Co. with a patent date of October 1884 and serial number 15, you can start by consulting firearms reference books, such as "The Blue Book of Gun Values" or "Flayderman's Guide to Antique American Firearms." Additionally, online forums and websites dedicated to antique firearms, like the International Society of Antique Firearms or GunsAmerica, may provide valuable insights. Lastly, you might consider reaching out to a firearms appraiser or a local gun shop that specializes in antiques for further assistance.
Go to an appraiser.
Perhaps a good place to start would be to find a copy of Flayderman's Guide to Antique American Firearms- you may be able to request a copy through your local library. This is a fairly comprehensive book with good descriptions and illustrations of thousands of antique firearms. You might also check for gun dealers in your area that know antique firearms, or check out a local gun show, where dealers in antique firearms have been neatly gathered in one spot for your convenience.
In firearms, antiques are LEGALLY defined as made prior to 1899, OR muzzleloading firearms. Newer than 1899, they are old, but not antiques. My best reference is Flayderman's Guide to Antique Firearms. You may also find a dealer or collector that can share some information with you. Check for gun shows in your area.
A great place to find an appraiser for vintage motorcycle helmets is to check with a local antique shop. If they couldn't help you, they might just be able to recommend someone for you.
A person who analyzes the value of something is called an appraiser.