A Mars-orbiting sub-millimeter sensor can be used to retrieve the magnetic field at low altitudes over large areas of significant planetary crustal magnetism of the surface of Mars from measurements of circularly polarized radiation emitted by the 368 GHz ground-state molecular oxygen absorption line. We design a full retrieval system for one example orbit to show the expected accuracies on the magnetic field components that one realization of such a Mars satellite mission could achieve. For one set of measurements around a tangent profile, we find that the two horizontal components of the magnetic field can be measured at about 200 nT error with a vertical resolution of around 4 km from 6 up to 70 km in tangent altitude. The error is similar regardless of the true strength of the magnetic field, and it can be reduced by repeated measurements over the same area. The method and some of its potential pitfalls are described and discussed.