Carbon nanotubes (CNTs) have extraordinary electronic properties owing to the unique band structure of graphene and their one-dimensional nature. Their small size and correspondingly small capacitances make them candidates for novel high-frequency devices with cut-off frequencies approaching one terahertz, but their high individual impedance hampers measurements of their high-frequency transport properties. In this dissertation, I describe the fabrication of carbon nanotube Schottky diodes on high-frequency compatible substrates and the measurement of their rectification at frequencies up to 40GHz as a method of examining the high-frequency transport of individual CNTs despite their high impedance. The frequency dependence of the rectified signal is then used to extract the Schottky junction capacitance as a function of applied bias and ambient doping and to look for resonances which might be a signature of a room-temperature Luttinger Liquid.