In this paper, two techniques are presented for enhancement of the radiation patterns of a line-fed rectangular patch antenna. The two techniques are based on removal of the substrate under the patch or etching spaced periodic dielectric or air holes in the substrate. The finite-difference time-domain (FDTD) method with perfect matched layer absorber (PML) is applied to determine the return loss, the effective dielectric constant, the input impedance, and the radiation pattern of the proposed structure. The results obtained are found to be in good agreement with the published measured data.