We propose a technique for electromagnetic shielding by combining zero-index metamaterials (ZIMs) and electromagnetic interference. Because the electric field inside the ZIMs can be zero, dielectric breakdown may be avoided, and the shield cover can be ultrathin, which may be less than 1% of the operating wavelength. In addition, we propose an energy concentrator made of ZIMs to confine the electromagnetic energy to a small zone based on the intrinsic refractive properties of ZIMs. This property may have potential in waveguiding applications.