From your request it is not clear what you mean by "sensitivity".
AM modulators have a response expressed as the proportion of carrier amplitude to the control voltage. Some modulators allow to control carrier level by a DC input voltage, others have only AC-coupled input (via a capacitor.)
If your AM modulator is an audio to RF device, you can use an audio generator with a variable output, and use an oscilloscope to observe the RF AM output.
If your device is a video to RF, you can use the same setup but instead of a typical audio input of 1 kHz, you can inject e.g. 1 MHz input signal.