To use the online sites you need to take the radio out of its mounting (to access the serial number).
However, as long as the radio is the original one which the car was supplied with, the manufacturer will have the code on a database related to the registration number of your car. All you need to do is to contact a main dealer for your make of vehicle and ask them to supply the code which is linked to your vehicle's registration. They can get the code from the manufacturer (so you won't have to remove the radio).
Up until recently I worked for a Ford main dealer. They usually charged £15 to supply a radio code.
Chris