This thesis focuses on model order reduction for non-linear magnetodynamic-mechanical systems. Using Maxwell's equations, a framework is established and validated with benchmarks. The study explores model order reduction and hyperreduction techniques, specifically DEIM and ECSW, evaluating them on academic and benchmark systems. Improvements to ECSW target non-linear domain areas and reduce post-processing costs. A practical use case with an active magnetic bearing demonstrates reduced-order models in monitoring scenarios, showcasing their potential to enhance simulation efficiency.