Simulation of devices including thin electromagnetic shields is nowadays a significant challenge because of the fine mesh required and the associated computation time. Recently, the transmission line theory used to model field propagation through thin conductive layers has been revised to solve shielding problems leading to the development of the Artificial Material Single Layer (AMSL) method. Initially developed for single-layer materials, this method has been extended to multilayer configurations. This paper presents an approach combining the homogenization of multilayer shields through energetic consideration and the second order AMSL method to accurately model metal composite for magnetic shielding applications. A comparison between the proposed approach and that of AMSL method for multilayers is proposed in terms of accuracy and computational time. These two discretization methods are also compared to the Impedance Network Boundary Conditions (INBCs) approach. On the frequency range of validity of the proposed method, the maximum relative error compared to experimental results is lower than 8.5%.