We have shown that a single layer of a 3D Zero Index Material (ZIM) has omnidirectional reflection properties. In the range between the electric plasma frequency and the magnetic plasma frequency, ZIM reflect radiation for all angles of incidence and polarization with reflectivities of .about.99%. In addition, with increasing angles of incidence, the reflecting band does not shift in frequency but actually widens. The operational bandwidth can be 100% or greater by increasing the separation between the electric and magnetic plasma frequencies. We have also shown that in the spectral region that allows the omnidirectional gap, ZIM can be used as the cladding of hollow waveguides with better performance than traditional hollow waveguides.