The role of relativistic effects on H-1 NMR chemical shifts of Sn-II and Pb-II hydrides is investigated by using fully relativistic DFT calculations. The stability of possible Pb-II hydride isomers is studied together with their H-1 NMR chemical shifts, which are predicted in the high-frequency region, up to 90 ppm. These H-1 signals are dictated by sizable relativistic contributions due to spin orbit coupling at the heavy atom and can be as large as 80 ppm for a hydrogen atom bound to Pb-II. Such high-frequency H-1 NMR chemical shifts of Pb-II hydride resonances cannot be detected in the H-1 NMR spectra with standard experimental setup. Extended NMR spectral ranges are thus suggested for studies of Pb-II compounds. Modulation of spin orbit relativistic contribution to H-1 NMR chemical shift is found to be important also in the experimentally known Sn-II hydrides. Because the H-1 NMR chemical shifts were found to be rather sensitive to the changes in the coordination sphere of the central metal in both Sn-II and Pb-II hydrides, their application for structural investigation is suggested.