An electronic device may communicate with an external device and may include one or more phased antenna arrays that transmit and receive a beam of millimeter wave signals. Beam steering circuitry may be coupled to the phased antenna array and may be adjusted to steer a direction of the beam. Control circuitry may control the beam steering circuitry to sweep the beam of millimeter wave signals over multiple beam directions. The control circuitry may gather wireless performance data and may compare the wireless performance metric data at each beam direction in the sweep prior to gathering wireless performance metric data at other beam directions in the sweep. The first beam direction in the sweep may be selected based on an initial position of the external device and/or based on sensor data gathered by the control circuitry.