Map matching and registration are essential tasks in robotics for localisation and integration of multi-session or multi-robot data. Traditional methods rely on cameras or LiDARs to capture visual or geometric information but struggle in challenging conditions like smoke or dust. Magnetometers, on the other hand, detect magnetic fields, revealing features invisible to other sensors and remaining robust in such environments. In this paper, we introduce Mag-Match, a novel method for extracting and describing features in 3D magnetic vector field maps to register different maps of the same area. Our feature descriptor, based on higher-order derivatives of magnetic field maps, is invariant to global orientation, eliminating the need for gravity-aligned mapping. To obtain these higher-order derivatives map-wide given point-wise magnetometer data, we leverage a physics-informed Gaussian Process to perform efficient and recursive probabilistic inference of both the magnetic field and its derivatives. We evaluate Mag-Match in simulated and real-world experiments against a SIFT-based approach, demonstrating accurate map-to-map, robot-to-map, and robot-to-robot transformations - even without initial gravitational alignment.