The paper provides an overview on the past research activities and summarizes the main results on the study aimed at design and implementation of an online method for diagnostics of shielding effectiveness for real conductive shields. The review starts with the results of theoretical investigations on shielding electromagnetic fields with structurally irregular low permeability enclosures in quasi-statics and resonant modes. Then we address the motivation for and list the main features of a novel hybrid simulation method we designed for quasi-statics. Inspired by the theoretical advances and promising experimental results, we propose the prototype method for online diagnostics of shielding effectiveness of electromagnetic enclosures. Finally, we discuss the means and approaches for practical implementation of the proposed method in an intellectual self-diagnostic system.