A display calibration system may be used to calibrate a display. The display calibration system may have an image sensor that captures images of the display. An electrically controllable tunable filter such as an electrically tunable liquid crystal birefringence cell filter may be used to produce various wavelength-dependent filter characteristics in accordance with a variety of different filter settings. Control circuitry in the display calibration system may be used to adjust the filter to implement one or more color matching functions or to produce other desired filter characteristics for the display calibration system. The image sensor may measure light emitted from the display while the control circuitry is adjusting the filter. The control circuitry may then process the measured light to produce calibration data for the display. The calibration data may be loaded into the display by the control circuitry to calibrate the display.