Call your local law enforcement office and ask them to run it through NCIC for you. They will need the serial number, manufacturer, model, and caliber. This is important, since the same number may have been used by different manufacturers. In some cases you will be required to take the gun to the law enforcement office so that they may confiscate the firearm if it is stolen.
The state of Florida offers an online database of stolen firearms to the general public but it only contains firearms stolen in the state of Florida. Firearms stolen in other states will not result in a positive match.
Another option is user submitted databases. Such databases are not all encompassing as they are not linked with NCIC, but still worth a look.