A model was recently introduced to describe the complex electrical conductivity and high-frequency dielectric constant of isotropic clayey porous materials. We generalized that approach to the case of anisotropic and tight hydrocarbon-bearing shales and mudrocks by introducing tensorial versions of formation factor and tortuosity. In-phase and quadrature conductivity tensors have common eigenvectors, but the eigenvectors of the dielectric tensor may be different due to influence of the solid phase at high frequencies. In-phase and quadrature contributions to complex electrical conductivity depend on saturation, salinity, porosity, temperature, and cation exchange capacity (alternatively, specific surface area) of the porous material. Kerogen is likely to have a negligible contribution to the cation exchange capacity of the material because all exchangeable sites in the functional groups of organic matter may have been polymerized during diagenesis. An anisotropic experiment is performed to validate some of the properties described by the proposed model, especially to verify that the electrical anisotropy factor is the same for in-phase and quadrature conductivities. We used two samples from the Bakken formation. Experimental data confirm the validity of the model. Also, the range of values for cation exchange capacity determined when implementing the new model with experimental data agree with the known range of cation exchange capacity for the Bakken shale. Measurements indicate that the bulk-space tortuosity in the direction normal to bedding plane can be higher than 100.