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We present design methodologies for directive millimeter-wave antennas using free-formed three-dimensional (3-D) electromagnetic bandgap (EBG) structures. Dispersion characteristics of 3-D EBGs have been computed by finite-difference time-domain (FDTD) simulations and the designed EBGs have been fabricated by using the extrusion free-forming technique. The fabricated EBG structures have been measured and integrated with a waveguide feed to form a Fabry-Perot cavity antenna. The prototype antenna demonstrated 10deg to 14deg beamwidths with measured gain of 13 dBi. The woodpile EBG antenna achieved a narrow beamwidth without resorting to complex arrays or bulky reflectors, which would make the antenna well-suited for millimeter-wave broadband mobile communications, imaging and space applications.