Rectangular-coaxial (recta-coax) transmission lines fabricated through a three-dimensional micromachining process are presented. These lines, are shown to have significant advantages over competing integrated transmission lines such as microstrip and coplanar waveguides. Design equations are presented for impedance, loss, and frequency range. The equations are confirmed with simulations and measurements. The quality factor of shorted lambda/4 resonators is measured to be 156 at 60 GHz. This corresponds to a line loss of 0.353 dB/cm. Advantages of these lines for passive millimeter-wave circuits including ease of signal routing, high isolation, and signal crossovers are demonstrated with realized lines and couplers.