Results derived from empirical analyses on the stability of climate coalitions are usually very sensitive to the large uncertainties associated with the benefits and costs of climate policies. This paper provides the methodology of Stability Likelihood that links uncertainty about benefits and costs of climate change to the stability analysis of coalitions in a stochastic, empirical setting. We show that the concept of Stability Likelihood improves upon the robustness and interpretation of stability analysis. Our numerical application is based on a modified version of the climate model STACO. It turns out that the only non-trivial coalition structure with a relatively high Stability Likelihood (around 25 percent) is a coalition between the European Union and Japan, though quantitative results depend especially on the variance in regional benefits from abatement.