LiNbO3 (LN) or LiTaO3 (LT) thin plates bonded to quartz are novel types of layered substrates for temperature-compensated surface acoustic wave (TCSAW) devices. In SAW resonators with Al electrodes arranged on LT/quartz and LN/quartz substrates, improved temperature behavior due to opposite signs of temperature coefficients of frequency (TCF) in quartz substrates and LT or LN plates can be combined with high Q -factors if the quartz orientation is optimized. The quartz orientation areas that enabled high Q -factors were deduced from analyzing the quartz anisotropy and the characteristics of shear horizontally (SH) polarized waves were calculated in the optimal orientations as functions of the quartz cut angle and plate thickness. The simulation results illustrated by contour plots of the wave characteristics revealed the presence of zero lines on the plots demonstrating TCFs at resonant (TCFR) and antiresonant (TCFA) frequencies in both layered structures. The strong quartz anisotropy explained anomalous temperature behavior of SAW resonators and the existence of LT/quartz structures with TCFA = TCFR facilitating the design of SAW devices with improved thermal stability in the passband. In the LT/quartz structures, two TCFs vanished simultaneously at certain plate thickness and quartz orientation, while in the LN/quartz zero lines did not intersect but low TCF = -(10-20) ppm/°C combined with electromechanical coupling exceeding 18% were obtained numerically in some structures. The effect of inverting the propagation direction or cut angle in one of the combined materials on the wave characteristics was discussed and numerically estimated.