The role of magnetic perturbations generated by filaments in the scrape-off layer is investigated by performing simulations of 3D seeded filaments with an electromagnetic numerical code which includes sheath boundary conditions. Depending on the plasma β, three smoothly connecting regimes were identified: an electrostatic regime where the magnetic field is substantially unaffected by the motion of the filament, an intermediate regime where the magnetic field is excited but relaxes within the filament's lifetime and an electromagnetic regime where the frozen-in condition is well satisfied. The electromagnetic effects are found to have a significant impact on the filament dynamics at values of β relevant for fusion devices, including increased midplane radial velocity, bending of the filament and braiding of magnetic field lines. Importantly, a finite Alfvén speed can allow electrical disconnection of the target and the upstream part of the filament, thus removing the slowing down effect associated with the sheath and producing faster filaments and more intense cross-field transport in perturbations that were affected by the sheath in the β = 0 limit.