Two methods for the mapping of ocean surface currents from satellite measurements of sea level and future current vectors are presented and contrasted. Both methods rely on the linear and Gaussian analysis frameworkwith different levels of covariance definitions. The first method separately maps sea level and currents with single-scale covariance functions and leads to estimates of the geostrophic and ageostrophic circulations. The second maps both measurements simultaneously and projects the circulation onto 4 contributions: geostrophic, ageostrophic rotary, ageostrophic divergent and inertial. When compared to the first method, the second mapping moderately improves the resolution of geostrophic currents but significantly improves estimates of the ageostrophic circulation, in particular near-inertial oscillations. This method offers promising perspectives for reconstructions of the ocean surface circulation. Even the hourly dynamics can be reconstructed from measurements made locally every few days because nearby measurements are coherent enough to help fill the gaps. Based on numerical simulation of ocean surface currents, the proposed SKIM mission that combines a nadir altimeter and a Doppler scatterometer with a 300 km wide swath (with a mean revisit time of 3 days) would allow the reconstruction of 50% of the near-inertial variance around an 18 hour period of oscillation.