  Low-loss microwave components are used in many superconducting resonant
circuits from multiplexed readouts of low-temperature detector arrays to
quantum bits. Two-level system defects in amorphous dielectric materials cause
excess energy loss. In an effort to improve capacitor components, we have used
optical lithography and micromachining techniques to develop superconducting
parallel-plate capacitors in which lossy dielectrics are replaced by vacuum
gaps. Resonance measurements at 50 mK on lumped LC circuits that incorporate
these vacuum-gap capacitors (VGCs) reveal loss tangents at low powers as low as
4x10^{-5}, significantly lower than with capacitors using amorphous
dielectrics. VGCs are structurally robust, small, and easily scaled to
capacitance values above 100 pF.
