A resonator antenna made from a complex artificial surface and a metallic ground plane is described. The complex surface is realized using a woodpile electromagnetic bandgap (EBG) material, which is shown to have a frequency dependent reflection plane location. A highly directive radiation pattern is created due to the angle-dependent attenuation of the resonator antenna coupling to free space. The antenna has the advantages of low height, low loss, and low sidelobes. It is shown that the directivity can be varied over a fixed range by changing the aperture size of the device, with the maximum directivity determined by both the feed element and EBG material properties. The complete bandgap for the woodpile EBG material is confirmed from a band diagram, and its properties as a complex surface are investigated through transmission calculation and measurement. The design of the antenna is described, and two means of exciting the resonator, a microstrip patch and a double slot, are investigated. Theoretical results for these two antennas are calculated the using finite-difference time-domain and are shown to be in good agreement with measured results.