Find a book with sn's published for the weapon you have (if it exists). Go to the maker's web site and see if they have a sn look up function. Go to Proofhouse.com
Look up at proofhouse.com
You find a published list of serial numbers for the maker.
proofhouse.com
try: proofhouse.com/winchester/index.html
You can look up serial numbers at Proofhouse.com
Depends on the serial number... Look up Winchester serial numbers..
Proofhouse.com has Colt serial numbers you can look up
Proofhouse.com has Colt serial numbers you can look up
Proofhouse.com has sn tables you look up
In books written about the company that made it. On line.
Proofhouse.com
IIRC, Cornell Publications has what you want.