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We analyze microwave cavity perturbation methods, and show that the techniqueis an excellent, precision method to study the dynamic magnetic and dielectricresponse in the $GHz$ frequency range. Using superconducting cavities, weobtain exceptionally high precision and sensitivity for measurements ofrelative changes. A dynamic electromagnetic susceptibility$\tilde{\zeta}(T)=\zeta ^{\prime}+i\zeta ^{\prime \prime}$ is introduced, whichis obtained from the measured parameters: the shift of cavity resonantfrequency $\delta f$ and quality factor $Q$. We focus on the case of aspherical sample placed at the center of a cylindrical cavity resonant in the$TE_{011}$ mode. Depending on the sample characteristics, the magneticpermeability $\tilde{\mu}$, the dielectric permittivity $\tilde{\epsilon}$ andthe complex conductivity $\tilde{\sigma}$ can be extracted from$\tilde{\zeta}_{H}$. A full spherical wave analysis of the cavity perturbationis given. This analysis has led to the observation of new phenomena in novellow dimensional materials.Comment: 16 pages, 5 figure

Precision microwave dielectric and magnetic susceptibility measurements of correlated electronic materials using superconducting cavities