Nowadays, communication technologies form an essential part of our everyday lives. Antenna systems receive thus more and more attention from both industrial and academic actors. These modern technologies are increasingly complex, and require fast prototyping and benchmarking in their design process. Numerical methods play a key role in that perspective, by providing an accurate estimation of the performance at low cost. However, the computation time and memory required by these electromagnetic simulators remain prohibitively high for certain classes of problems. This thesis focuses on the development of specialized numerical methods, with the goal of mitigating their computational cost. The proposed methods are physics-based optimizations of the Method of Moments, which has been ubiquitous in the analysis of planar and metallic antenna structures. Motivated by the recent and exciting advances in the field of metasurface antennas, the main part of the dissertation is dedicated to planar structures. The contributions range from essentially theoretical results, such as mathematical links between well-established antenna theory results; to efficient solvers exploiting the Contour-FFT for the analysis of large planar arbitrary arrays; to the development of miniaturized shielded arrays for localization applications.