The thesis discusses micromagnetic simulation studies on high-frequency magnetic dynamics in three-dimensional ferromagnetic nanoarchitectures made of interconnected magnetic nanowire networks. Such artificial magnetic materials with nanoscale features have recently emerged as a vivid topic of research, as their geometry has a decisive impact on their magnetic properties. By studying their static magnetization structure, we find that these systems display a behavior analogous to that of 3D artificial spin ice lattices, with frustrated interactions and the emergence of monopole-like defect structures at the wires' intersection points. Our simulations reveal a high activity of these defect sites in the magnonic high-frequency spectrum. We study various 3D nanoarchitectures and show that their geometry and magnetization state results in characteristic high-frequency signatures. Controlling these features could open new pathways for magnonics research and reprogrammable magnetic metamaterials.