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Low-profile antennas comprising a horizontal dipole above a high-impedance surface are analyzed. The emphasis of this paper is on the additional resonances of the radiating structure caused by surface waves propagating on the high-impedance surface. It is shown that such resonances can be favorably used for broadening the bandwidth of the antenna. The phenomenon is thoroughly modeled by exploiting a parallel between the HIS structure and a waveguide resonator. In the second part of the paper we discuss homogenized approaches for modeling the radiating properties of the antenna with emphasis to the phenomenon discussed in the first part. As it turns out, it is necessary to take into account the spatially dispersive properties of high-impedance surfaces, and most of the simplified models commonly used for analyzing high-impedance surface based antennas fail in predicting the discussed resonance mode.