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A design is suggested for testing equipment of antennas operating in short millimeter waveband (SMW, f= 60...300 GHz). Testing is based on amplitude and phase measurements over a plane in the near field of the antenna under test. Design solutions are offered for critical subsystems, including the mechanical scanner, the radio-measurement subsystem and the automatic control subsystem. The approach should allow near-field testing of SMW antennas to achieve high accuracies comparable to those of similar testing of centimeter waveband antennas.