Relatively simple and accurate closed form Uniform Geometrical Theory of Diffraction (UTD) solutions are obtained for describing the radiated and surface wave fields, respectively, which are excited by sources near or on thin, planar, canonical two-dimensional (2-D) double positive/double negative (DPS/DNG) material discontinuities. Unlike most previous works, which analyze the plane wave scattering by such DPS structures via the Wiener-Hopf (W-H) or Maliuzhinets methods, the present development can also treat problems of the radiation by and coupling between antennas near or on finite material coatings on large metallic platforms. The latter is made possible mainly through the introduction of important higher-order UTD slope diffraction terms which are developed here in addition to first-order UTD. The present solutions are simpler to use because, in part, they do not contain the complicated split functions of the W-H solutions nor the complex Maliuzhinets functions. Unlike the latter methods based on approximate boundary conditions, the present solutions, which are developed via a heuristic spectral synthesis approach, recover the proper local plane wave Fresnel reflection and transmission coefficients and surface wave constants of the DPS/DNG material. They also include the presence of backward surface waves in DNG media. Besides being asymptotic solutions of the wave equation, the present UTD diffracted fields satisfy reciprocity, the radiation condition, boundary conditions on the conductor, and the Karp-Karal lemma which dictates that the first-order UTD space waves vanish on a material interface.