This paper links climate science with sovereign risk assessment to produce a single forward-looking measure of country-level climate change risk. We combine the Network for Greening the Financial System (NGFS) climate scenarios with a sovereign credit ratings model to simulate the impact of climate change on credit ratings, cost of debt and probability of default. For the first time, we extend beyond the physical risks of extreme weather events to explicitly incorporate risks associated with transitioning the global economy towards Net Zero. Across the sample of 48 countries and under a scenario of high (low) physical and transition risks, we find average downgrades of 3.9 (2.7) notches and mean increases in the cost of debt of 123 (76) basis points and default probability of 10.4% (6.2%). Counter-intuitively, ratings, default probability, and cost of debt appear insensitive to scenarios in some countries, with important implications for the usefulness of NGFS scenarios across central banks.