What is the opposite of your forearm?
Since your forearm is the lower part of your arm, the other part is usually called your upper arm.
If it is a Side by Side like my Western Long Range Gun, pop off the forearm - mine is marked in three places: the wood of the forearm, the metal of the forearm, and on the action. My Model 37 has the serial number stamped on the front of the reciever, opposite the slide for the pump. It is in the area between the magazine tube and the barrell.