We present a general method for continuously measuring and compensating for offsets (due to residual amplitude modulation, parasitic resonances, or electronic offset voltages, for example) in frequency stabilization systems. The spectral power distribution of the oscillator waveform is modified by amplitude-modulated sidebands, and the error signal is corrected to null the induced periodic lock-point shifts. We demonstrate significant improvements to the frequency stability of standards based on cryogenic optical resonators and molecular iodine.