The world's coastal areas are increasingly at risk of coastal flooding due to sea-level rise (SLR). We present a novel global dataset of extreme sea levels, the Coastal Dataset for the Evaluation of Climate Impact (CoDEC), which can be used to accurately map the impact of climate change on coastal regions around the world. The third generation Global Tide and Surge Model (GTSM), with a coastal resolution of 2.5 km (1.25 km in Europe), was used to simulate extreme sea levels for the ERA5 climate reanalysis from 1979 to 2017, as well as for future climate scenarios from 2040 to 2100. The validation against observed sea levels demonstrated a good performance, and the annual maxima had a mean bias (MB) of -0.04 m, which is 50% lower than the MB of the previous GTSR dataset. By the end of the century (2071-2100), it is projected that the 1 in 10-year water levels will have increased 0.34 m on average for RCP4.5, while some locations may experience increases of up to 0.5 m. The change in return levels is largely driven by SLR, although at some locations changes in storms surges and interaction with tides amplify the impact of SLR with changes up to 0.2 m. By presenting an application of the CoDEC dataset to the city of Copenhagen, we demonstrate how climate impact indicators derived from simulation can contribute to an understanding of climate impact on a local scale. Moreover, the CoDEC output locations are designed to be used as boundary conditions for regional models, and we envisage that they will be used for dynamic downscaling.