The climatological frequency of stratospheric sudden warming events (SSWs) is an important dynamical characteristic of the extratropical stratosphere. However, modern climate models have difficulties in simulating this frequency, with many models either considerably under- or overestimating the observational estimates. Past research has found that models with a higher upper lid tend to simulate a higher and more realistic number of SSWs. The present study revisits this issue and investigates causes for biases in the simulated SSW frequency from the CMIP5 and CMIP6 models. It is found that variations in the frequency are closely related to (1) the strength of the polar vortex and (2) the upward propagating wave activity in the stratosphere. While it is difficult to explain the variations in the polar vortex strength from the available model output, the stratospheric wave activity is influenced by different aspects of the climatological mean state of the atmosphere in the lower stratosphere. We further find that models with a finer vertical resolution in the stratosphere are overall more realistic: vertical resolution is associated with a smaller cold bias above the extratropical tropopause, more upward propagating wave activity in the lower stratosphere, and a higher frequency of SSWs. We conclude that not only a high model lid but also a fine vertical resolution in the stratosphere is important for simulating the dynamical variability of the stratosphere.