We assess the accuracy and spatial resolution of the surface water and ocean topography (SWOT) swath altimeter for deriving marine gravity anomalies. The analysis is performed at the Foundation Seamounts in the South Pacific where we developed a highly accurate gravity field by combining the long‐wavelength (>40 km) gravity field derived from previous nadir altimeters with the shorter wavelength gravity field from the seafloor topography as constrained by the ship gravity. In this region, the sea surface slope (SSS) of the ocean variability is 50–100 times smaller than the slope signal of the seamounts so can be ignored in the analysis. Each SWOT cycle can deliver SSS accurately with a standard deviation of 2.6 µrad and a spatial resolution of 14 km at typical sea state (significant wave height 4 m), with accuracy diminishing at high significant wave heights (e.g., exceeds 6 m). Averaging repeated SWOT measurements improves the accuracy and resolution. For example, we expect that averaging just 10 repeats (7 months) results in accuracy/resolution that matches the best marine gravity maps based on 230 months of nadir altimetry. With a mission lasting over a year, SWOT promises a substantial leap in marine gravity accuracy and resolution, uncovering previously uncharted details of the seafloor, including thousands of uncharted seamounts.