Ocean wave climate is an important area of research, particularly in the context of extremes driven by tropical cyclones (TC). We can now simulate global climate at resolutions sufficient to resolve TCs and for durations long enough to explore climatological changes. Both the devastating 2017 North Atlantic hurricane season and growing evidence for the connection between TC activity and increasing ocean temperature motivate investigation of possible future changes. We present two simulated 50-year global wave climate data sets under possible future warming scenarios characterized by +1.5°C and +2.0°C stabilized global mean temperatures that capture the effects of TCs. Differences in extreme wave climate between these possible scenarios and present-day conditions appear to be significant in many areas, particularly those affected by TCs. However, for computational feasibility, simulations of this kind rely on fixed sea surface temperatures, so we also investigate and elucidate effects from the lack of a dynamic ocean by simulating waves from a number of recent hurricanes and comparing output to observations. We conclude that atmosphere-only forcing is likely to result in an overestimate of extreme wind speeds and wave heights in TC-affected regions. More ensemble studies are needed to help elucidate detailed processes relevant to extreme wave climate, and important community projects such as the Coordinated Wave Climate Intercomparison Project (COWCLIP) should be supported.