Waveguides and scattering devices are made from a pair of slabs, at least one slab being either an "epsilon-negative (ENG)" layer in which the real part of permittivity is assumed to be negative while its permeability has positive real part, or a "mu-negative (MNG)" layer that has the real part of its permeability negative but its permittivity has positive real part. The juxtaposition and pairing of such ENG and MNG slabs under certain conditions lead to some unusual features, such as resonance, complete tunneling, zero reflection and transparency. Such materials also may be configured to provide guided modes in a waveguide having special features such as mono-modality in thick waveguides and the presence of TE modes with no cut-off thickness in thin parallel-plate waveguides. Using equivalent transmission-line models, the conditions for the resonance, complete tunneling and transparency are described as well as the field behavior in these resonant paired structures. A "matched" lossless ENG-MNG pair is configured to provide "ideal" image displacement and image reconstruction.