This paper proposes a new way to measure the shielding effectiveness of ferromagnetic shields. The procedure combines an experimental characterization of the shielding material and numerical simulations. In a first case, magnetic hysteresis is reduced to a series of equivalent B -H linear relations through an optimization procedure that is applied to a measured set of symmetric minor loops, and an equivalent multilayer linear medium is defined through a subsequent iterative procedure. In a second case, magnetic hysteresis is reduced to a simple B-H nonlinear relation, obtaining an equivalent nonlinear shield. In both cases, the obtained results are compared with the direct measurements of the shielding effectiveness at different operating frequencies, showing good agreement and the validity of the proposed method. A comparison and a discussion on the harmonic content of the attenuated field for the investigated shield geometry are reported. The same analysis is carried out for a basic diffusion problem, comparing the results with those obtained by the use of a Preisach model.