Material interfaces occur at various length scales and may exhibit significantly different properties than the surrounding bulk. Regarding microscale processes, grain and phase boundaries are of particular interest. Due to their distinct atomic arrangement, these defects affect transport processes in the continuum under consideration and, hence, the effective macroscale transport coefficients. In this work, we lay particular focus on the transport of electric charges and the associated macroscale conductivity tensors. Building upon the work [1], we extend well-established energy-based computational multiscale formulations for bulk material to continua featuring microscale material interfaces. We embed the generalised formulation into a multiscale finite element code and discuss elementary academic boundary value problems focusing, amongst others, on the size dependency of the effective material response. In a second step, we demonstrate the applicability and usefulness of the proposed formulation by a detailed study of experimental data [2]. Specifically speaking, we consider the Andrews method that has been used in the materials science community since the early 60s to evaluate the effect of grain boundary resistivity in experiments. Making use of the proposed multiscale approach, we provide a solid theoretical foundation to the Andrews method, discuss its applicability and tacit assumptions involved, and resolve its core limitations. References [1] Güzel D., Kaiser T., Menzel A., A computational multiscale approach towards the modelling of microstructures with material interfaces in electrical conductors. Mathematics and Mechanics of Solids, Vol. 30 (2), 247-266, 2025, doi: 10.1177/10812865231202721 [2] Güzel D., Kaiser T., Bishara H., Dehm G., Menzel A., Revisiting Andrews method and grain boundary resistivity from a computational multiscale perspective. Mechanics of Materials, Vol. 198 (1), 105115, 2024, doi: 10.1016/j.mechmat.2024.105115