The finite element method (FEM) is applied to calculate the screening effect of electromagnetic radiation through screens with periodic perforations. In this procedure, screens of large extent with complex but periodic geometry are replaced during the FEM simulation by sheets representing anisotropic impedance boundary conditions. The homogenized anisotropic impedance boundary conditions are calculated from a single unit cell of the screen by using the finite element method. The FEM is modified to handle the new anisotropic impedance boundary condition. Replacing large screens with an impedance boundary condition reduces the size of the finite element mesh and allows more complex structures to be simulated. While the procedure is approximate, it does provide good accuracy to determine levels of EMC/EMI radiation in complex electronic equipment. The method is applied to compute the radiation emanating from a real-life electronic printed circuit board enclosed in a real-life computer cabinet