The serial number is obviously stamped in. Don't worry about scratching it off or whatever. Should be on the receiver or the barrel near the breach. Once that rust is on there it'll be nearly impossible to get it off without taking off some of the finish. Idk how bad the rust is. I've got muskets that rust pretty easily and I've taken it off with some rough sandpaper like 200 grit and then polish it with emery cloth or machinists cloth. What you do, pull it out of a pond lol?