In the coming decades, the frequency of coastal flooding will increase due to sea-level rise and changes in climate extremes. We force the Global Tide and Surge Model (GTSM) with a climate model ensemble from the CMIP6 High Resolution Model Intercomparison Project (HighResMIP) to produce global projections of extreme sea levels (defined as tides and storm surge) from 1950 to 2050. This is the first time that an ensemble of global ~25km resolution climate models is used for this purpose, which increases the credibility of projected storm surges. Here we validate the historical simulations (1985-2014) against the ERA5 climate reanalysis. The overall performance of the HighResMIP ensemble is good with mean bias smaller than 0.1 m. However, there is a strong large-scale spatial bias. Future projections for the high emission SSP5-8.5 scenario indicate changes up to 0.1 m or 20% in 10-year return period surge level from 1951-1980 to 2021-2050. Increases are seen in parts of the coastline of the Caribbean, Madagascar and Mozambique, Alaska, and northern Australia, whereas the Mediterranean region may see a decrease. The full dataset underlying this analysis, including timeseries and statistics, is openly available on the Climate Data Store and can be used to inform broad-scale assessment of coastal impacts under future climate change.