A head-mounted device may have a left display and a right display that provide respective left and right images. Left and right optical combiner systems may be configured to pass real-world light to left and right eye boxes while directing the left and right images respectively to the left and right eye boxes. Misalignment of the left and right images with respect to the left and right eye boxes may be detected using gaze tracking systems, using cameras such as front-facing cameras in conjunction with a database of known real-world object properties, using visual inertial odometry systems formed from cameras and inertial measurement units, or using one or more sensors in a portable head-mounted device case or other item with a receptacle configured to receive a head-mounted device. Compensating adjustments may be made to the images based on the measured misalignment.