In this study, we investigated whether and how the storm surge induced by Hurricane Katrina could change if a similar event occurred in a future warmer climate. In addition, we evaluated the sensitivity of the changes to atmospheric forcing resolution. Climate model simulations of Hurricane Katrina at 27 km, 4.5 km, and 3 km resolutions were used to drive storm surge simulations in historical and future climates using the ADvanced CIRCulation (ADCIRC) model. We found that peak surge height increased significantly in the future, regardless of atmospheric forcing resolution. However, the future projection is 22% greater under the 3 km forcing, typical of convection-permitting regional models, compared to the 27 km forcing, typical of state-of-the-art global climate models. Additionally, the spatial extent of the future change is highly sensitive to forcing resolution, extending most broadly under the 27 km forcing. Furthermore, we found that storm surge duration decreases in the future under all forcing resolutions due to increased tropical cyclone translation speed and decreased lifetime over ocean. However, the future change in the surge duration is sensitive to the forcing resolution, decreasing by 31% under the 27 km forcing and 6% under the 3 km forcing.