While sea level rise is one of the most likely consequences of climate change, the provoked costs remain highly uncertain. Based on a block-maxima approach, we provide a stochastic framework to estimate the increase of expected damages with sea level rise as well as with meteorological changes and demonstrate the application to two case studies. In addition, the uncertainty of the damage estimations due to the stochastic nature of extreme events is studied. Starting with the probability distribution of extreme flood levels, we calculate the distribution of implied damages in a specific region employing stage-damage functions. Universal relations of the expected damages and their standard deviation, which demonstrate the importance of the shape of the damage function, are provided. We also calculate how flood protection reduces the damages leading to a more complex picture, where the extreme value behavior plays a fundamental role.