The ever rising operating frequencies and complexity of emerging electronic devices are making it increasingly hard for the design engineer to meet all specifications. The multiscale nature and stringent design constraints of state-of-the-art technologies can only be tackled by relying on computer aided design tools that solve the underlying physical laws, i.e., Maxwell’s equations, with ever increasing accuracy. In this doctoral research, I will develop electromagnetic modeling techniques based on the differential surface admittance (DSA) operator and boundary element methods to achieve efficient and accurate numerical tools to characterize novel interconnect technologies and support advanced processing techniques. The strategy taken in this project is to rely on a strong mathematical foundation, i.e., a spectral analysis approach, to investigate open questions in terms of convergence and applicability of the DSA method. Based on these fundamental results, I will then develop advanced instances of the operator that overcome its current limitations. In two-dimensions, the focus will be on cross-sectional analysis of interconnects, enabling the inclusion of curvilinear shapes and unbounded domains for the accurate characterization of, e.g., rounded corners and substrate layers, respectively. For three-dimensional configurations, the aim is to implement the inclusion of magnetic materials and to extend the arsenal of supported shapes to layered cylinders, prisms and polyhedra.