A millimeter waveguide is disclosed which includes: a first single crystal substrate having a groove therein; a conductor film on a surface of said groove and a surface of said first single crystal substrate connected to said surface of said groove; a second single crystal substrate covering said conductor film; and a microstrip line on a surface of said second single crystal substrate, exposed to a cavity in said groove. A protruding portion may be formed on a bottom surface of the groove. The microstrip line including foundation (nickel chromium) and conductive (gold) layers may be formed on a surface of the groove. A protruding portion may be formed on the second single crystal substrate, wherein the height of this protruding portion is less than the depth of the groove. A millimeter waveguide for a resonator is also disclosed wherein a cavity is formed in substrates with grounding conductive layers on surfaces of the cavity, a probe extending from a microstrip line on a top surface of the substrates. Similar millimeter waveguide is also disclosed wherein the probe is replaced by magnetic field coupling structure. A circuit apparatus is also disclosed which comprises the millimeter waveguide apparatus mentioned above mentioned and an active circuit fixed on the millimeter waveguide apparatus.