Abstract The Surface Water Ocean Topography mission (SWOT), scheduled for launch in 2021, is the first space-borne radar interferometer capable of providing wide-swath height maps of water surfaces with centimetric precision. In addition to its primary objectives in oceanography and hydrography, the SWOT instrument offers opportunities for other applications. Here, we explore the feasibility of sea ice freeboard and sea surface height retrievals in the ice-covered oceans from SWOT data. The quality of SWOT height estimates depends on the backscatter strength and number of samples used for multi-looking. We use near-nadir radar backscatter estimates from sea ice and water over the range of SWOT incidence angles to simulate SWOT height maps and assess the retrieval precision under different backscatter, surface type and roughness conditions. Unlike wind-roughened open water, the available observations suggest that backscatter over sea ice has a moderate dependence on look angle (specularity), and the backscatter of younger, flatter sea ice has a greater degree of specularity than older, more deformed and colder sea ice. To achieve a similar freeboard precision to conventional altimeters (∼3 cm) requires averaging over 15–40 km² in the near- to mid-swath and 90–175 km² in the far-swath for lower northern latitudes (<65°N), and 9–18 km² in the near- to mid-swath and 30–50 km² in the far-swath over Southern hemisphere ice. Compared to a typical altimeter grid cell used for time and area averages (∼25 km × 25 km or 625 km²), this represents an improvement in resolution of 3–70 fold between the near- and far-swath. Overall, the results suggest that SWOT has the potential to provide unique new insights in the high-latitude oceans by providing two-dimensional maps of sea ice thickness and dynamic ocean topography at higher resolution, in both space and time, than has previously been possible.