We show that magnetic field and eddy current calculations in axisymmetric systems can still be performed two-dimensionally if the axial symmetry is disturbed by small displacements perpendicular to the symmetry axis of the magnetic field source. Such a situation occurs for instance when the rotor of a permanent magnetic bearing oscillates transversally to the rotation axis. By using appropriately adapted 2-D finite element programs our method allows for instance the computation of the eddy current losses in certain devices used for the damping of such oscillations. Numerical results are compared with experimental data.