A finite element methodology is proposed for the efficient full-wave computational analysis of interconnects and integrated passives for system-on-chip (SoC) and system-in-package (SiP) applications. These structures are characterized by drastic variations in feature size along different directions in space, that result in severe ill-conditioning of conventional finite element solution approaches for their electromagnetic characterization. The proposed methodology overcomes this problem by decomposing the solution into an asymptotic frequency expansion which reduces the electrodynamic problem into a series of coupled static field problems. The approach is more complicated in the case of a lossy conductor and a proper modification is introduced to take the frequency dependent losses of the system into account. Finally, an asymptotic technique that fits perfectly into the framework of the asymptotic solution, is applied to stabilize the solution, while an alternative screening technique inside the conductor could be also used. Preliminary numerical studies are presented to illustrate the attributes of the proposed methodology.