A new system has been developed for determining precisely the Q-factor of an X-band open resonator. The new system differs from previous systems in its use of an injection-locked phase-shifting technique to provide electronically a ± π/4 phase shift for Q-factor measurement. The ± π/4 phase change is produced at an i.f. frequency with a total uncertainy that is an order of magnitude lower than is possible with conventional phase shifters. The phase-shifting technique employs a crystal-controlled reference oscillator and a second oscillator whose free running frequency is close to that of the reference oscillator. The output of the second oscillator is injection-locked to the 8th harmonic of the reference-oscillator signal. A π/4 phase shift on the output of the second locked oscillator is achieved by unlocking it from one cycle of the 8th harmonic of the reference oscillator and relocking it to an adjacent cycle. The new system uses single-sideband homodyne detection. Single-sideband modulation is achieved by using the open resonator as a high-Q filter to remove all but the required sideband from the output of a double-sideband modulator. The new system incorporates the injection-locked phase-shifting technique and the homodyne detection system in a phase-locked loop to provide rapid Q-factor measurements.