[en] The shielding performance of perforated magnetic shields for electric power applications is described. The shielding of an axisymmetric induction heating device is studied as a function of frequency, number of perforations and dimensions of the perforations. From the numerical point of view, the perforations cause the numerical model to be 3D. A numerical optimisation is carried out to find the optimal geometry with respect to the shielding factor and the volume of the shield. For the optimisation, two approaches are presented. The first approach is fast and easy-to-implement, but has limited accuracy. It uses a classical 2D axisymmetric model where the perforations are approximated by ‘axisymmetric air gaps’ resulting in a segmented shield. It is shown how to modify the 2D model to obtain results that are similar to the ones of a 3D model. The second approach is more accurate although quite fast, but more difficult to implement. It combines a 3D thin- shell finite element model with the unmodified 2D model in a space mapping optimisation algorithm. The validation of both models is based on experimental work for an unperforated shield and for the optimised perforated shield.