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Nine in ten major outages in the US have been caused by hurricanes. Long-term outage risk is a function of climate change-triggered shifts in hurricane frequency and intensity; yet projections of both remain highly uncertain. However, outage risk models do not account for the epistemic uncertainties in physics-based hurricane projections under climate change, largely due to the extreme computational complexity. Instead they use simple probabilistic assumptions to model such uncertainties. Here, we propose a transparent and efficient framework to, for the first time, bridge the physics-based hurricane projections and intricate outage risk models. We find that uncertainty in projections of the frequency of weaker storms explains over 95% of the uncertainty in outage projections; thus, reducing this uncertainty will greatly improve outage risk management. We also show that the expected annual fraction of affected customers exhibits large variances, warranting the adoption of robust resilience investment strategies and climate-informed regulatory frameworks.