We have used laser‐micromachined alumina substrates to build a three‐dimensional photonic band‐gap crystal. The rod‐based structure has a three‐dimensional full photonic band gap between 90 and 100 GHz. The high resistivity of alumina results in a typical attenuation rate of 15 dB per unit cell within the band gap. By removing material, we have built defects which can be used as millimeter‐wave cavity structures. The resulting quality (Q) factors of the millimeter‐wave cavity structures were as high as 1000 with a peak transmission of 10 dB below the incident signal. ©1995 American Institute of Physics.