Over the past decade, radio tomographic techniques have seen increasing use within space science, both in practice, with ionospheric reconstruction, and theoretically as a tool for remote sensing magnetospheric plasmas. The promise of this technique for use in the magnetosphere was greatly enhanced with the introduction of combined Faraday rotation and phase or group delay radio tomography. As measurables these techniques provide distributions in space and time of electron density ne and magnetic field $vec B$. Given these measured quantities, this paper provides a theoretical framework for further derivation of additional parameters, such as plasma temperature, based upon MHD relations. Additionally, we show how using the physical constraint $vec{nabla}$ ¿ $vec B$ = 0 to regularize the reconstructions of magnetic field yields superior reconstructions with fewer measurements and provides a physical and effective method for incorporating in situ magnetometer measurements. Specifically, we find that including this regularization often reduces RMS errors in magnetic field reconstructions by a factor of 3. This simple regularization, especially when combined with in situ magnetometer measurements, is so powerful that it may influence future designs of a magnetospheric tomography mission.