Nondestructive tests in microwave frequencies for dielectric parameters evaluation with high spatial resolution have a great significance in many fields of material science. In this paper, we present a new method for the dielectric parameter characterization based on the displacement of the multiresonance spectrum of the magnetostatic (MS) oscillations in a thin-film ferrite disk due to loading by a dielectric sample. The effect is manifested by shifting and widening of the MS spectrum that is dependent on the relative permittivity of the sample. The correlation between the MS spectrum characteristics is used in a postprocessing analysis to enhance the separability of noisy data and thereby increase the measurement accuracy. The experimental and numerical results have shown the ability to accurately evaluate the dielectric parameters of the load sample under consideration. The simplicity of the measurement in a wide range of operating frequencies along with nondestructive sensing with a subwavelength resolution of 100 $\mu \text{m}$ complies with the current requirements of scanning microwave microscopy.