The simulated stratospheric dynamics have been improved compared to previous generations in many climate models taking part in the Coupled Model Intercomparison Project Phase 6 (CMIP6). This was achieved by going from low to high‐top configurations, that is, increasing the atmospheric vertical resolution, raising the model lid height and including parameterization schemes, such as non‐orographic gravity wave drag (GWD), to simulate small‐scale processes. This also applies to the EC‐Earth model, for which comprehensive analysis is now possible thanks to outputs archived within the Dynamics and Variability Model Intercomparison Project (DynVarMIP). Here we analyze atmosphere‐only simulations and evaluate the stratospheric dynamics of low‐top CMIP5 and high‐top CMIP6 configurations of EC‐Earth against the MERRA‐2 and ERA5 reanalyses. This allows us to identify and interpret model biases in the atmospheric component and to highlight deficiencies needed to be addressed in future model versions. We find substantial improvements in the simulation of the stratosphere in the CMIP6 configuration, both in the tropical and extratropical regions. The zonal wind momentum budget in the tropical stratosphere is much improved in the high‐top configuration. Seasonal variability of both models is qualitatively similar to the reanalysis, but for the low‐top model this is likely due to compensating errors, as its intraseasonal variability is less realistic. The non‐orographic GWD forcing is weak in the high‐top model and this limits the realism of the tropical stratosphere variability. We point to persisting issues in the stratosphere of EC‐Earth that should be tackled to improve hemispheric‐scale circulation and variability.