High-performance algorithms and software have been designed for fast 2D forward modeling and inversion of high-frequency electromagnetic logs to recover the patterns of electrical conductivity and relative permittivity (dielectric constant) of rocks. Forward modeling implies linear representation, with regard to eddy current, of attenuations and phase shifts of electromagnetic fields propagating in 2D conducting formations. In order to improve the modeling quality, the background model is chosen proceeding from the eddy current pattern in a heterogeneous subsurface. The inverse solution is obtained by pseudoinversion of the sensitivity matrix of relative amplitudes and phases. Joint 2D inversion of phase shifts and attenuations improves the reliability of the inferred spatial conductivity distribution and allows estimating permittivity. The reported numerical experiments on inversion of synthetic and field EM logs prove the possibility of estimating the permittivity of complex terrigenous and carbonate reservoirs with water- and oil-filled porosity.