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Projected changes in the Northern Hemisphere stratospheric polar vortex are analyzed using Climate Model Intercomparison Project Phase 6 experiments. Previous studies showed that projections of the wintertime zonally averaged polar vortex strength diverge widely between climate models with no agreement on the sign of change, and that this uncertainty contributes to the regional climate change uncertainty. Here, we show that there remains large uncertainty in the projected strength of the polar vortex in experiments with global warming levels ranging from moderate (SSP245 runs) to large (Abrupt‐4xCO₂runs), and that the uncertainty maximizes in winter. Partitioning of the uncertainty in wintertime polar vortex strength projections reveals that, by the end of the 21st century, model uncertainty contributes half of the total uncertainty, with scenario uncertainty contributing only 10%. Regression analysis shows that up to 20% of the intermodel spread in projected precipitation over the Iberian Peninsula and northwestern US, and 20%–30% in near‐surface temperature over western US and northern Eurasian, can be associated with the spread in vortex strength projections after accounting for global warming. While changes in the magnitude and sign of the zonally averaged vortex strength are uncertain, most models (>95%) predict an eastward shift of the vortex by 8°–20° degrees in longitude relative to its historical location with the magnitude of the shift increasing for larger global warming levels. There is less agreement across models on a latitudinal shift, whose direction and magnitude correlate with changes in the zonally averaged vortex strength so that vortex weakening/strengthening corresponds to a southward/poleward shift.