The present invention relates to the field of radio-frequency (RF) waveguides. More specifically, the present invention pertains to a method and apparatus that provides ultra-low-loss RF waveguide structures targeted between approximately 300 GHz and approximately 30 THz. The RF waveguide includes a hollow core and a flexible honeycomb, periodic-bandgap structure surrounding the hollow core. The flexible honeycomb, periodic-bandgap structure is formed of a plurality of tubes formed of a dielectric material such as of low-loss quartz, polyethylene, or high-resistivity silicon. Using the RF waveguide, a user may attach a terahertz signal source to the waveguide and pass signals through the waveguide, while a terahertz signal receiver receives the signals.