National energy system models play a crucial role in climate policy. However, they often overlook environmental impacts beyond territorial greenhouse gas emissions. Here we evaluate a territorial net-zero carbon dioxide emissions energy scenario for Switzerland coupled with life cycle assessment to quantify non-domestic environmental burdens. We highlight the limitations of considering only territorial emissions. Indeed, even if domestic greenhouse gas emissions are reduced to net zero by 2050, 2 to 5 megatonnes of carbon dioxide equivalent per year persist abroad due to imports and energy-related infrastructure. These extra-territorial emissions are influenced by global climate policies. Additionally, broadening the scope of environmental indicators is crucial as more countries pursue net-zero goals. Our findings highlight trade-offs, showing how environmental impacts other than those on climate change (ecosystem impacts, air pollution, natural resource use) could increase and shift beyond Switzerland as the country electrifies its economy.