The capability of measuring the complex permittivity of tissues has the potential to provide valuable new insights to inform medical assessment and diagnosis. However, existing electrical impedance approaches have practical limitations when aiming to measure tissues' anisotropy with accuracy. Here we present new methods that overcome the limitations of previous approaches by modeling the anisotropy in both the resistivity and reactivity of tissues measured in three or more different directions. These new methods are validated with numerical simulations and in situ experiments on healthy ovine skeletal muscle. The obtained data between 3 kHz and 1 MHz are also made publicly available in the supplementary information.