In this thesis, an analysis of wave propagation in symmetric planar waveguides or sandwich structures is studied with specific emphasis on the properties of the materials used in these structures. We consider four different models for the waveguide problems and discuss them for the propagation of electromagnetic surface and guided waves under various situations. These proposed models may offer possible applications to design and fabricate new sandwich or waveguide structures operating at microwave frequencies. In our first theoretical model, we analyse transverse electric (TE) surface waves for a plasma medium bounded by two ferrite films. The characteristic equations for the field components are derived and a dispersion relation is analytically obtained by using boundary conditions for the tangential field components. Numerical analysis shows the plots of effective wave index with surface wave frequency for different thicknesses and number densities of the plasma medium, and also for the different values of the dielectric constant of the ferrite films. In the second theoretical model, the characteristics of nonlinear TE surface waves are analysed in a plasma medium bounded by Kerr-type double-negative (DNG) metamaterials (MTMs). In this connection, the electric and the magnetic field components, the dispersion relation, and the power flow in the direction of propagation are derived. The dispersion relation and the power flow are numerically analysed for variations in different parameters of the guiding structure. We also examine the special cases for nonlinear single-negative (SNG) MTMs. The third model deals with the propagation of nonlinear TE surface waves in a structure consisting of a ferrite slab sandwiched between a Kerr-type DNG metamaterial (MTM). In addition to a DNG MTM, two special cases with nonlinear SNG MTMs have also been discussed. The dispersion relations are obtained by applying the boundary conditions to the tangential field components of each layer. The propagation characteristics are plotted numerically for the effective wave index versus propagation frequency. In the subsequent model, we discuss the propagation of electromagnetic waves in a high-temperature superconducting parallel-plate waveguide filled with an indefinite medium. In this connection, we obtain dispersion relations of transverse electric (TE) and transverse magnetic (TM) wave modes. We numerically analyse the regions of propagation/nonpropagation for the different cases of TE and TM wave modes by plotting the phase velocity against the propagation frequency for different cases.