In this work, the shear horizontal surface acoustic wave (SH-SAW) resonators were demonstrated on 15° YXLiNbO3/SiO2/sapphire (LiNbO3-on-sapphire, LNOS) substrate. Compared to the reported gigahertz SAW resonators based on piezoelectric heterogeneous substrates, the fabricated resonator in this work exhibits a state-of-the-art electromechanical coupling coefficient (k2) of 42.2\%, a maximum Bode-Q (Qmax) of 1457 and an excellent figure of merit (k2×Qmax) of 615. Besides, several methods for suppressing transverse modes were implemented and compared. Tilted interdigital-transducers combined with the apodization technique can suppress the transverse modes more thoroughly while maintaining decent Q values. Overall, SAW devices based on the LNOS substrate have great potential for RF filters with low insertion loss, steep skirts, and wide bandwidth.