Electromagnetic Interference (EMI) in electronic devices is one of the major challenges in the design of high-speed electronic packages. These challenges are intensified by the increase in the level of system integration and the ever-increasing operating frequency of microprocessors. EMI takes place at different levels including the package, board, component and chip. The physical mechanism behind electromagnetic interference is the coupling of energy between different EM sources. This coupling can be either conducted or radiated. However, regardless of the coupling mechanism, surface currents are needed to support the field that eventually radiates, which constitute the electromagnetic interference in the first place. Minimizing these surface currents is considered a fundamental and critical step in minimizing EMI. In this work, novel strategies are proposed to confine surface currents in enclosures and cavities. Unlike the traditional use of lossy materials and absorbers, which suffers from considerable disadvantages including mechanical and thermal reliability leading to limited life time, we consider the use of electromagnetic Band Gap (EBG) structures which are inherently suited for surface current suppression. The effectiveness of the EBG as an EMI suppresser in enclosures, chasses and cavities will be demonstrated using numerical simulations.