Layered-medium integral-equation (LMIE) methods that can confront the multiscale problems encountered in electromagnetic modeling of electronic packages are presented. The methods include (i) an impedance-boundary condition (IBC) formulation for modeling conductor thickness, roughness, and finite conductivity, (ii) non-radiating lumped-port models for extracting network parameters, and (iii) FFT based iterative and hierarchical-matrix (ℋ-matrix) based direct algorithms for efficiently solving the resulting systems of equations. The methods are used to analyze increasingly higher fidelity models of a benchmark packaging interconnect structure; the results are validated with measurements; and the tradeoff between increased model fidelity and computational costs are quantified.