This paper analyses the risk of extreme coastal events in major European coastal cities using a stochastic diffusion model that is calibrated with the worst case emission scenario from the Intergovernmental Panel for Climate Change (IPCC), i.e., the representative concentration pathway (RCP) 8.5. The model incorporates uncertainty in the sea-level rise (SLR) distribution. Expected mean annual losses are calculated for 19 European coastal cities, together with two risk measures: the Value at Risk (VaR) and the Expected Shortfall (ES). Both measures are well-known in financial economics and enable us to calculate the impact of the worst SLR paths under uncertainty. The results presented here can serve as valuable inputs for cities in deciding how much risk they are willing to accept, and consequently how much adaptation they need depending on the risk aversion of their decision-makers.