We develop a deep neural network (DNN) modeling methodology to predict the radiated emissions of a shielding enclosure in terms of its aperture attributes including aperture shape, size, pitch, and quantity. The target structure is the inside of a three-dimensional (3D) enclosure comprised of perfect electric conductor (PEC) boundaries with dimensions of a desktop personal computer (PC) containing thermal dissipation apertures on the surface of its back panel. The DNN model is developed to compute the radar cross section (RCS) as a function of aperture attributes and to enable the efficient assessment of the PC’s electromagnetic compatibility (EMC). To generate training data for machine learning (ML), we implement the modified equivalent current approximation (MECA) method and validate it against analytical methods and a commercial field-solver. We use MECA to compute RCS data for approximately 55,000 experiments across a wide range of aperture attributes. We examine numerous DNN models across parameters such as number of layers and nodes per layer, activation function, optimization algorithm, loss function, batch size, and epoch, to identify the optimal DNN model based on (a) accuracy, (b) computation time, and (c) memory usage. Results show excellent agreement between MECA and DNN predictions for previously unseen cases.