A new local method for magnetic resonance electrical properties tomography (EPT), dubbed transverse-EPT (T-EPT), is introduced. This approach iteratively optimizes the dielectric properties (conductivity and permittivity) and the z-component of the electric field strength, exploiting the locally E-polarized field structure typically present in the midplane of a birdcage radiofrequency (RF) coil. In contrast to conventional Helmholtz-based EPT, T-EPT does not impose homogeneity assumptions on the object and requires only first order differentiation operators, which makes the method more accurate near tissue boundaries and more noise robust. Additionally, in contrast to integral equation-based approaches, estimation of the incident fields is not required. The EPT approach is derived from Maxwell’s equations and evaluated on simulated data of a realistic tuned RF coil model to demonstrate its potential.