Significant research exists regarding the successful implementation of hollow waveguides for the low-loss transmission of infrared radiation in applications ranging from laser power delivery to spectroscopy. With the continued development of terahertz (THz) technologies and applications, it is often advantageous to have a waveguide for the transmission of THz radiation. This study focuses on the fabrication of novel silver-coated polytetrafluoroethylene (PTFE) waveguides for the transmission of terahertz radiation. The hollow structure described in this paper is made by depositing a thin film of Ag on the outer surface of a dielectric tube. This is in contrast to depositing metallic and dielectric thin film coatings on the inner surface of capillary tubing as is commonly done for IR and some THz transmissive waveguides. In this work, the Teflon tubing itself is the dielectric layer that is used to enhance the reflectivity of the Ag. Theoretical loss calculations will be presented and compared to the loss obtained for the guides measured at THz frequencies. In addition the spectra of the guides in the infrared region are also measured as a means to study the uniformity of the Teflon "layer" and to confirm the wall thickness of the Teflon tubing. The surface topography of the silver / PTFE waveguides is obtained and the resulting surface roughness related scattering losses are calculated. The implications of the terahertz fiber for applications ranging from nondestructive evaluation (NDE), security, and medical imaging are briefly discussed.