Since we know nothing about your grandfather and less about the gun any information is purely guess work. How old was your grandfather (mine died in 1938) and when did he obtain the gun? At first glance, the gun appears to be a "Trade Brand Name" shotgun. I have only one listing for the name LIBERTY alone, no LIBERTY ARMS CO. And that gun was made by the Davenport Arms Company and the gun in the photograph was not. The gun in the photograph appears to be nickel plated and highly engraved. "Trade Brand Name" guns were either blued or in a few cases had a color case hardened finish and almost never engraved. The gun in the photograph, I would guess is either Spanish or Italian made. There's a listing in the Blue Book Of Gun Values for the name Liberty, again no Arms and no mention of a single barrel break open breech loader. This name was used on imported guns imported by K.B.I. INC. OF Harrisburg,PA (1997 to 2003). I can make and educated guess as to value. The value of old single barrel break open shotguns depends on their condition, the amount of original finish remaining on the metal and wood as well as the mechanical condition. This gun appears to be in excellent condition and with the nickel finish and engraving, might bring as much as $150 if sold at auction. However, sentimental value can't be calculated. Maybe someone else might have more information.