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We assess the reliability of an indirect method of inferring the atmospheric response to projected Arctic sea ice loss from CMIP5 simulations, by comparing the response inferred from the indirect method to that explicitly simulated in sea ice perturbation experiments. We find that the indirect approach works well in winter, but has limited utility in the other seasons. We then apply a modified version of the indirect method to 11 CMIP5 models to reveal the robust and non‐robust aspects of the wintertime atmospheric response to projected Arctic sea ice loss. Despite limitations of the indirect method, we identify a robust enhancement of the Siberian High, weakening of the Icelandic Low, weakening of the westerly wind on the poleward flank of the eddy‐driven jet, strengthening of the subtropical jet, and weakening of the stratospheric polar vortex. The surface air temperature response to projected Arctic sea ice loss over mid‐latitude continents is non‐robust across the models. Plain Language Summary: The continued melt of Arctic sea ice will likely affect weather and climate in places far from the Arctic. To better understand the far‐flung implications of sea ice loss, scientists can perform bespoke climate model experiments in which sea ice is reduced, but all other climate drivers are fixed. In our paper, we test the reliability of an indirect method to infer the atmospheric response to sea ice loss, which makes use of a large set of climate model experiments originally performed for other purposes. We find that the indirect approach works well in winter, but not so well in other seasons. We then apply the indirect method to 11 climate models to reveal the robust and non‐robust aspects of the wintertime atmospheric response to projected Arctic sea ice loss—the largest such comparison to date. We found that the models agreed on quite a few aspects of the response, including warming over the Arctic, regional surface pressure changes over Siberia and Iceland, and a slowing of the mid‐latitude jet stream. On the other hand, the models disagreed on whether surface air temperatures over Europe, North America, and East Asia will warm or cool in response to future Arctic sea ice loss. Key Points: Wintertime atmospheric response to projected Arctic sea‐ice loss can be well‐estimated indirectly from CMIP5 simulationsRobust changes across models including stronger Siberian High, weaker Icelandic Low, slower eddy‐driven jet and faster subtropical jetNon‐robust changes in surface air temperature over mid‐latitude continents and sea level pressure over the North Pacific [ABSTRACT FROM AUTHOR]