Geostrophic strain deforms upper-ocean tracer gradients, but its frontogenetic effect on sea surface temperature fronts is controlled by the component of deformation acting as cross-front compression. Conventional gridded altimetry attenuates much of the 15–100 km geostrophic velocity-gradient field that organizes this strain–front coupling, leading to underestimation of submesoscale strain and frontogenetic compression. Here we combine SWOT-derived geostrophic velocities with daily GHRSST/MUR SST to diagnose front-normal strain acting on SST fronts and its alignment with the local SST-gradient direction over the global SWOT swath record. Relative to conventional altimetry, SWOT resolves stronger strain and intensified frontogenesis and frontolysis in western boundary-current extensions, the Antarctic Circumpolar Current, the Agulhas system, and eddy–front interaction regions. Separating frontogenetic capacity from alignment-dependent efficiency shows that strong strain and sharp SST gradients provide only the potential for frontogenesis, with frontogenesis or frontolysis reflecting the orientation of cross-front compression relative to the SST front. These results identify where balanced geostrophic deformation preconditions SST frontal sharpening, providing a satellite-based basis for locating regions where frontal dynamics may favor enhanced vertical exchange.