Ensuring energy security and mitigating climate change are key energy policy priorities. The recent Intergovernmental Panel on Climate Change Working Group III report emphasized that climate policies can deliver energy security as a co-benefit, in large part through reducing energy imports. Using five state-of-the-art global energy-economy models and eight long-term scenarios, we show that although deep cuts in greenhouse gas emissions would reduce energy imports, the reverse is not true: ambitious policies constraining energy imports would have an insignificant impact on climate change. Restricting imports of all fuels would lower twenty-first-century emissions by only 2-15% against the Baseline scenario as compared with a 70% reduction in a 450 stabilization scenario. Restricting only oil imports would have virtually no impact on emissions. The modelled energy independence targets could be achieved at policy costs comparable to those of existing climate pledges but a fraction of the cost of limiting global warming to 2 °C.