In this article, an aperture antenna excited by a waveguide with a circular cross-section and covered with a dielectric plate was analyzed via simulation calculation and verified via measurements. The influence of the geometrical and electromagnetic parameters of the dielectric plate on the reflection coefficient S11 of the antenna opening was systematically analyzed. The geometrical parameters taken in this analysis are the thickness d and the width/length h1/h2 of the dielectric plate. The electromagnetic parameters used in this analysis are the real and the imaginary part of permittivity (εr, tan δ) and the electrical conductivity of the dielectric plate (σ). The simulation calculation and analysis included other structural and electromagnetic parameters of the dielectric plate (density of the radome material, relative permeability, and magnetic loss tangent (ρ, µr, and tan δµ, respectively)), but the results show that in the range of real values of these parameters for the materials used for the dielectric plate, they had no significant influence on the reflection coefficient. The results show that impedance-matched antennas with very low values of the reflection coefficients S11 at the resonant frequency can be realized by changing the geometrical and electromagnetic parameters of the dielectric plate material. The results are presented for a circular aperture antenna on a planar grounded plane with a dielectric plate on the opening, and the achieved lowest values of the S11 parameter were −45.17 dB (simulated) and −43.93 dB (measured) at the frequencies of 1.7820 GHz and 1.7550 GHz, respectively. The estimated values of the dielectric plate parameters in this case are thickness d = 11.08 mm (0.67 λ); width x length of grounded plane and dielectric plate h1 x h2 = 423 × 450 mm2 (2.51 × 2.67 λ); relative permittivity 2.5, tan δ = 0.09, μr = 1, tan δμ = 0.00, ρ = 1200 kg·m−3; and electrical conductivity σ = 0 S/m. The simulation calculation results were verified by measuring the reflection coefficient S11 on the created laboratory model of the aperture antenna with the dielectric plate and showed a very good match.