Methods to evaluate the eddy current amplitude induced in a shield are presented. This is used to assess the effect of those currents on the efficiency of coils in an magnetic particle imaging scanner. The example of a shielded drive coil is introduced and a finite element method and a boundary element method are used to evaluate the loss of efficiency of the coil when operated with ac signals. The calculation needed to implement the boundary element method is detailed, which offers an analytic representation of the phenomena. This, in turn, improves the available knowledge to make design decision at the scanner level. The results of both methods are found to be similar, when the fields generated by a coil with different shields are compared. However, the calculation cost of the boundary element method is far inferior. The boundary element method calculation shows that, besides the used frequency, the geometry of the system, and the shielding material, there is little to be done to increase the shielded-coil performance. In addition, the results for this methods may be integrated into an optimization scheme to integrate them for the design of coils.Index Terms-Boundary element method (BEM), eddy current, electromagnet design, finite element method (FEM), magnetic particle imaging (MPI), shielding.