Optical properties of a high-temperature superconductor in the near-zero-permittivity operation range are theoretically investigated. Investigations are performed through the calculations of optical reflectance over three model structures. First, the calculated wavelength-dependent reflectance for a bulk superconductor occupying half-space shows that the threshold wavelength is strongly influenced by the angle of incidence and the polarization of wave. Second, the reflectance response in a single superconducting slab has a peak at the threshold wavelength for the transverse magnetic (TM) wave, whereas the shape of the peak is very sensitive to the angle of incidence. Finally, reflectance is calculated for a superconductor- dielectric bilayer structure. The results illustrate that the dielectric substrate has a pronounced effect on the reflectance response for both TM and transverse electric waves.