Call Remington at 1-800-243-9700 during normal business hours. They can tell you the age.
Lots of us have had these old family 11s.
Value, depending on area, is probably less than $400, and if it's in round shape, less than $200. As with all shotguns that predate WWII, a visit to the smith is in order. A new set of rings, springs, buffer and an expert cleaning of the innards will set it up for your grandkids.
Enjoy....