The three-dimensional finite-difference time-domain (FDTD) method and the two-dimensional quasi-static formulation have been used to calculate the characteristic impedance and the microwave effective index of coplanar waveguide structures on Lithium Niobate ($LiNBO_3$) single crystal substrates with a yttria-stabilized zirconia (YSZ) or $SiO_2$ buffer layer. The results shown can be a good source to predict the modulator characteristics. The effects of the thin buffer layer and anisotropy of the $LiNBO_3$ crystal (x-cut and z-cut) are discussed. The comparison between the FDTD and quasi-static results shows good agreement. In this paper, the efficient modeling technique of the FDTD method for the coplanar waveguide (CPW) structures based on an anisotropic substrate with a thin buffer layer is developed.