A test system may include a master test station and slave test stations. The test stations may receive devices under test such as portable wireless electronic devices. Each test station may have adjustable antenna structures coupled to test equipment. The adjustable antenna structures may include antenna support structures on which test antennas are mounted and rail along which the antenna support structures and test antennas are moved by a pneumatic positioner. A rotatable platform may be provided in each test station to support the device under test in that test station. By making a series of over-the-air test measurements in the master test station while adjusting the antenna system and device positioning system, a satisfactory location for the active test antenna and device position may be identified. This configuration may then be used in performing single-point over-the-air tests in the slave test stations.