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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‐4xCO2 runs), 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. Plain Language Summary: Previous studies showed that changes in the strength of the winds in the Northern Hemisphere wintertime stratosphere, the so‐called polar vortex, can affect near‐surface winds and precipitation on various timescales. However, climate models do not agree on whether the polar vortex will weaken or strengthen during the 21st century. Here, we use Climate Model Intercomparison Project Phase 6 experiments to better understand how the polar vortex will respond to future greenhouse gas emissions. We show that half of the uncertainty in the vortex strength projections by the end of the 21st century is due to climate model errors (model uncertainty). We show that the uncertainty in the vortex strength projections is linked to the uncertainty in projected precipitation over the Iberian Peninsula and northwestern US and projected near‐surface temperature over the western US and northern Eurasia. Most models predict an eastward shift of the vortex relative to its historical location but we do not detect any influence of the vortex longitudinal shift on surface precipitation and temperatures. There is less agreement across models on a latitudinal shift, whose direction and magnitude correlate with changes in the vortex strength so that vortex weakening/strengthening corresponds to a southward/poleward shift of the vortex. Key Points: Model uncertainty contributes half of the total uncertainty in the projected strength of the Northern winter stratospheric polar vortexUncertainty in the projected polar vortex strength is linked to uncertainty in projected regional surface temperature and precipitationMost climate models project an eastward shift of the Northern winter stratospheric polar vortex [ABSTRACT FROM AUTHOR]