Managing the magnetic signatures of complex naval and aerospace platforms is a critical challenge, as integrating low-signature subsystems can still reveal electromagnetic vulnerabilities. This chapter details numerical simulations that predict these behaviors early, preventing costly redesigns. The central difficulty is modeling disparate scales—from massive hulls to small cable traces and propulsion motors. To address this, the chapter introduces a hybrid approach that couples Finite Element Method (FEM) solvers with Spatio-Temporal Harmonic Analysis (SHA). By using tools such as “balloon boundaries” and “infinite elements” within commercial software, engineers can simulate open-boundary problems in unbounded space. The chapter validates these numerical predictions against experimental data and explores source separation techniques to ensure accuracy. Whether using cylindrical sensor arrays or spheroidal multipole analysis, these methods provide the precision needed for magnetic silencing.