Coastal flooding is often caused by extreme events, such as storm surges. In this study, improved physical models have been used to simulate the climate system and storm surges, and to predict the effect of increased atmospheric concentrations of greenhouse gases on the surges. In agreement with previous studies, this work indicates that the changes in atmospheric storminess and the higher time-average sea-level predicted for the end of the twenty-first century will lead to changes in the height of water levels measured relative to the present day tide. However, the details of these projections differ somewhat from earlier assessments. Uncertainty in projections of future extreme water levels arise from uncertainty in the amount and timing of future greenhouse gas emissions, uncertainty in the physical models used to simulate the climate system and from the natural variability of the system. The total uncertainty has not yet been reliably quantified and achieving this should be a priority for future research.