Near-THz gyrotrons are of interest for applications such as remote sensing, materials processing, and dynamic nuclear polarization (DNP) enhanced nuclear magnetic resonance (NMR) applications. We are setting up a gyrotron test-bed based on a Cryomagnetics 12-T cryogen-free, 3-inch warm-bore, superconducting magnet to investigate second- and higher-harmonic gyrotrons operating at frequencies up to 1 THz. The first experiments are designed to operate at the second harmonic at frequencies up to 600 GHz and powers in the kilowatt range. A triode electron gun operating at 30-60 kV and 0.5-2 A will be used. A Vlasov-type output coupler designed using geometric optics will be used to extract the output power as a quasi-Gaussian beam. An interaction cavity based on the TE 15,2 mode with an effective length of about 1 cm and a Q of 7400 has been designed. The ability to tune the output frequency is important for many applications and is an important objective of this research. Calculations of the expected continuous and step tuning achievable with this cavity will be discussed. Other design calculations and the status of the experiment will be presented.