The propagation characteristics of the conductor-backed coplanar waveguide are analyzed by using the spectral domain approach(SDA)and the finite difference time domain(FDTD)method. Effective dielectric constants and characteristic impedances of the conductor-backed coplanar waveguide have been computed as a function of frequency. The results are shown in figures. Also, the coupling characteristics of microstrip lines through a slot, reflection, transmission and coupled coefficients have been computed. The results are compared with those which are obtained by another method. Both of them are in good agreement.