The connection between changes in the North Atlantic Oscillation (NAO) and the sea level over the northwest European continental shelf is investigated for the period 1955--2000 using a two-dimensional model of tides and storm surges. There is a clear spatial pattern in the correlation between sea level and the NAO on a winter-mean timescale. Correlations are positive (>0.8) in the northeast and negative (<-0.7) in the south. The sensitivity of the sea level to the NAO is strongest in the southern North Sea (up to 96 mm per unit NAO index), where most of the sensitivity is present also in the non-hydrostatic component of sea level. The relationships are validated using observed data recorded at coastal tide gauges.