In this paper, the frequency stability of high-Q electrostatically-actuated MEMS oscillators with cubic restoring forces, and its relation with the amplitude, the phase and the shape of the excitation waveform, is studied. The influence on close-to-the carrier frequency noise of additive processes (such as thermomechanical noise) or parametric processes (bias voltage fluctuations, feedback phase fluctuations, feedback level fluctuations) is taken into account. It is shown that the optimal operating conditions of electrostatically-actuated MEMS oscillators are highly waveform-dependent, a factor that is largely overlooked in the existing literature. This simulation-based study covers the cases of harmonic and pulsed excitation of a parallel-plate capacitive MEMS resonator.