Climate change threatens the resource adequacy of future power systems. Existing research and practice lack frameworks for identifying decarbonization pathways that are robust to climate-related uncertainty. We create such an analytical framework, then use it to assess the robustness of alternative pathways to achieving 60\% emissions reductions from 2022 levels by 2040 for the Western U.S. power system. Our framework integrates power system planning and resource adequacy models with 100 climate realizations from a large climate ensemble. Climate realizations drive electricity demand; thermal plant availability; and wind, solar, and hydropower generation. Among five initial decarbonization pathways, all exhibit modest to significant resource adequacy failures under climate realizations in 2040, but certain pathways experience significantly less resource adequacy failures at little additional cost relative to other pathways. By identifying and planning for an extreme climate realization that drives the largest resource adequacy failures across our pathways, we produce a new decarbonization pathway that has no resource adequacy failures under any climate realizations. Our framework can help planners adapt to climate change, and offers a unique bridge between energy system and climate modelling.