In this thesis, by utilising the inverse scattering problems approach, it was tried to improve the sensitivity in measuring the dielectric constants of the materials with microwave resonator cavities. The direct problem involves measurement of frequency shift and electric field/power values. The inverse problem aims to calculate the dielectric constant with the data obtained from the direct problem. First of all, the accuracy of the rectangular and cylindrical cavities operating in the S-band in the material perturbation method was compared with simulations, and how their sensitivity changes depending on the increasing frequency and dielectric constant was observed. Afterwards, dielectric constants were calculated by measuring the frequency shifts in the scope of the direct problem with a rectangular aluminium cavity for 3 different materials at the frequency of 1.254 GHz. However, this traditional method has a high error rate especially for samples with large dielectric constant or volume. For this reason, a measurement method based on Newton-Raphson iteration approach has been proposed. This proposed method uses power or electric field measurements at a particular frequency regardless of which mode is excited in the cavity. With the help of iterations based on an initial guess, the dielectric constant could be determined more precisely. Within the scope of this thesis, the results of the simulations performed with the Newton-Raphson method were given and the effect of the change of 3 different parameters of the method on the results was observed. In these simulations, iterations were carried out using electric field values at a certain number of points around the material. Finally, with the help of the spectrum analyzer, power measurements were taken from the 7-port aluminium cavity for the direct problem and the inverse scattering problem, which aims to recalculate the dielectric constant, was solved. More accurate results were obtained with the Newton-Raphson method.