A test system may include a wireless test chamber with metal walls lined with pyramidal absorbers. A trapdoor may be provided in a wall opening to accommodate a robotic arm. The robotic arm may have grippers that grip a device under test or a support structure that is supporting a device under test. The robotic arm may move the device under test to a docking station for automatic battery charging during testing. When it is desired to perform wireless tests on a device under test, the robotic arm may move the device under test through the trapdoor into an interior portion of the test chamber. A turntable and movable test antenna may be used to rotate the device under test while varying angular orientations between test antenna and device under test. Emitted radiation levels can be measured using a liquid filled phantom and test probe on a robotic arm.