We introduce a methodology for quantifying climate litigation risks stemming from insurers’ investment in fossil fuels-related assets. It builds on recent advances in liability attribution of climate warming damages to fossil fuel producers, obtaining the Carbon Majors Index (CMI) as a cumulative emission-weighted portfolio of major polluters’ stocks. We validate the CDI by showing that the percentage of fossil fuel investments is a significant determinant of the yearly exposure to the CMI. We compare linear losses from linear exposures and non-linear losses from Exposure CoVaR. The size of the large polluters’ possible losses from climate litigation is calibrated using losses of Tobacco companies after the US Tobacco Master Settlement Agreement. Our results show that linear and non-linear losses differ in size and ranking of institutions. This suggests the importance of a non-linear long-tail risks approach in assessing climate litigation risk for insurance.