Devastating floods due to Atlantic hurricanes are relatively rare events. However, the frequency of the most intense storms is likely to increase with rises in sea surface temperatures. Geoengineering by stratospheric sulfate aerosol injection cools the tropics relative to the polar regions, including the hurricane Main Development Region in the Atlantic, suggesting that geoengineering may mitigate hurricanes. We examine this hypothesis using eight earth system model simulations of climate under the Geoengineering Model Intercomparison Project (GeoMIP) G3 and G4 schemes that use stratospheric aerosols to reduce the radiative forcing under the Representative Concentration Pathway (RCP) 4.5 scenario. Global mean temperature increases are greatly ameliorated by geoengineering, and tropical temperature increases are at most half of those temperature increases in the RCP4.5. However, sulfate injection would have to double (to nearly 10 teragrams of SO2 per year) between 2020 and 2070 to balance the RCP4.5, approximately the equivalent of a 1991 Pinatubo eruption every 2 y, with consequent implications for stratospheric ozone. We project changes in storm frequencies using a temperature-dependent generalized extreme value statistical model calibrated by historical storm surges and observed temperatures since 1923. The number of storm surge events as big as the one caused by the 2005 Katrina hurricane are reduced by about 50% compared with no geoengineering, but this reduction is only marginally statistically significant. Nevertheless, when sea level rise differences in 2070 between the RCP4.5 and geoengineering are factored into coastal flood risk, we find that expected flood levels are reduced by about 40 cm for 5-y events and about halved for 50-y surges.