This study illustrates a methodology to assess the economic impacts of climate change at a city scale and benefits of adaptation, taking the case of sea level rise and storm surge risk in the city of Copenhagen, capital of Denmark. The approach is a simplified catastrophe risk assessment, to calculate the direct costs of storm surges under scenarios of sea level rise, coupled to an economic input-output (IO) model. The output is a risk assessment of the direct and indirect economic impacts of storm surge under climate change, including, for example, production and job losses and reconstruction duration, and the benefits of investment in upgraded sea defences. The simplified catastrophe risk assessment entails a statistical analysis of storm surge characteristics, geographical-information analysis of population and asset exposure combined with aggregated vulnerability information. For the city of Copenhagen, it is found that in absence of adaptation, sea level rise would significantly increase flood risks. Results call for the introduction of adaptation in long-term urban planning, as one part of a comprehensive strategy to manage the implications of climate change in the city. Mitigation policies can also aid adaptation by limiting the pace of future sea level rise.