An electronic device may be provided with a phased antenna array that radiates at a frequency greater than 10 GHz through a display. The array may include a dielectric resonator antenna having a dielectric column. The dielectric column may have a first surface mounted to a circuit board and a second surface that faces the display. A conductive cap may be formed on the second surface. The conductive cap may allow the dimensions of dielectric column to be reduced while still allowing the dielectric resonator antenna to cover a frequency band of interest. If desired, the phased antenna array may include multiple sets of dielectric resonator antennas for covering different frequency bands. The sets may have different dielectric column heights and/or different conductive cap sizes.