A new approach to the theoretical evaluation of the local dielectric properties of media that contain an organic dye acting as a nanoprobe is proposed. The method is checked so as to evaluate the dielectric properties of the host molecule in a supramolecular inclusion complex from the experimentally measured shift of the optical absorption spectrum of the guest molecules (dye) after the complex formation. Using the Onsager–Liptay model, the dielectric properties of the cucurbit[7]uril cavity was theoretically estimated by analyzing the experimentally measured shift of the absorption spectrum of 1-(3-ammoniopropyl)-4-[(E)-2-(3,4-dimethoxyphenyl)-ethenyl]-pyridinium dication of the dye after it forms a complex with cucurbit[7]uril in an aqueous solution. To parameterize the Onsager–Liptay equation, the positions of the absorption spectral maxima of the dye under study were experimentally measured in the following solvents with known dielectric and optical properties: methanol, ethanol, 1-propanol, 1-butanol, and water. When calculating molecular structures, dipole moments of the ground and excited states, and polarizability, the TD-DFT quantum chemical method with the CAM-B3LYP functional in the 6-311G(d,p) basis set was used within the Gamess (United States) software package. The obtained theoretical value of the effective dielectric permittivity of the cavity (about 13) is in good agreement with the published value.