Local air-sea interaction over the Mediterranean may amplify the effects of climate change. This study investigates the sensitivity of simulations of two different high impact weather events to changes in the specification of sea surface temperature (SST) using a regional atmospheric model. First we assess the impact of specifying SST from two reanalysis data sets with differing spatial resolution. The simulated tropical-like cyclone (TLC) is slightly stronger in the case of the lower resolution SST which is warmer over the formation region, most notably in the maximum rainfall which is ~7% higher. The differences in the two explosive cyclone simulations are negligible, most likely due to intensification occurring mainly over land. We then test the sensitivity of the storms to a range of SST anomalies. The TLC showed a clear trend of increasing storm intensity as SST rises. These results suggest that SST plays a direct role in determining the intensity of the storm. For the explosive cyclone there is no clear trend in dynamical intensity except for the highest warming anomalies. However, the rainfall increases with the magnitude of the SST anomaly. Our results suggest that extreme weather events over the Mediterranean will become more extreme if SST increases as the climate warms, assuming that upper air conditions do not change.