Major sudden stratospheric warmings (SSWs), vortex formation, and final breakdown dates are key highlight points of the stratospheric polar vortex. These phenomena are relevant for stratosphere‐troposphere coupling, which explains the interest in understanding their future changes. However, up to now, there is not a clear consensus on which projected changes to the polar vortex are robust, particularly in the Northern Hemisphere, possibly due to short data record or relatively moderate CO 2 forcing. The new simulations performed under the Coupled Model Intercomparison Project, Phase 6, together with the long daily data requirements of the DynVarMIP project in preindustrial and quadrupled CO 2 (4xCO 2 ) forcing simulations provide a new opportunity to revisit this topic by overcoming the limitations mentioned above. In this study, we analyze this new model output to document the change, if any, in the frequency of SSWs under 4xCO 2 forcing. Our analysis reveals a large disagreement across the models as to the sign of this change, even though most models show a statistically significant change. As for the near‐surface response to SSWs, the models, however, are in good agreement as to this signal over the North Atlantic: There is no indication of a change under 4xCO 2 forcing. Over the Pacific, however, the change is more uncertain, with some indication that there will be a larger mean response. Finally, the models show robust changes to the seasonal cycle in the stratosphere. Specifically, we find a longer duration of the stratospheric polar vortex and thus a longer season of stratosphere‐troposphere coupling.