A procedure for measuring the Q factor of a microwave composite acoustic resonator is described. The resonator consists of a relatively thick crystal plate and a piezoelectric film with electrodes that is deposited on the plate. The procedure is based on mathematical processing of the array of measurement data on the coefficient of the electromagnetic-wave reflection from the resonator structure connected to a microwave reflectometer. Via this procedure, it is possible to obtain data on the Q factor at the resonance and antiresonance frequencies.