Different methods for modeling the motions, torques, and losses in a permanent-magnet shaft coupling are studied. The containment shroud of the coupling is a homogeneous conducting cylinder. Its motion can be modeled by using the motional electromotive force (i.e. the v × B term). The moving-band technique is used for modeling the relative motion of the magnet cylinders of the coupling. Using the motional electromotive force for the shroud gives reliable results while the computational effort is kept at minimum. The stiffness and damping coefficients of the coupling are obtained from a numerical impulse response test.