A pillbox antenna is a linearly polarized, waveguide-fed, cylindrical reflector, sandwiched between parallel plates. It is well suited to be a base-station antenna for the millimeter-wave, local-to-multipoint distribution service (LMDS). We can form the reflector-surface profile to provide a shaped radiation pattern, such as a cosecant-squared pattern in elevation, and we can design the radiating aperture to provide a broad-beam azimuth pattern. In this article, we begin by discussing LMDS requirements for base-station antennas, and we then briefly compare pillbox antennas with other antennas. Next, we describe in detail a highly accurate and efficient procedure for designing a pillbox antenna, using a combination of ray-tracing theory and commercially available three-dimensional electromagnetic analysis software. In particular, we discuss methods for designing the reflector surface, the waveguide feed horn, the radiating aperture, the polarizer, and the radome. Measured results of a prototype antenna at 29.4 GHz compare very well with our predictions.