The first part of this paper describes the Meissner effect in superconductors which serves as the most definitive evidence for superconductivity. It is shown that the microwave perturbation technique may be used to demonstrate this effect. By measuring the changes of resonant frequency and inverse quality factor Q of a microwave cavity with a small volume of sample loading, the Meissner effect can be shown by using the Slater perturbation equation. The experimental system is described with details and the basic principle of each component discussed. The second part of this work describes the technique employed to do the actual measurements. The experiments were conducted on samples of Gallium Arsenide (GaAs) and lead zirconate titanate (PZT) to look for the possible high temperature superconductivity properties. Results of these experiments are presented and discussed. Conclusion and suggestions to future exploration are made.