The C-13 and Si-29 NMR signals of ligand atoms directly bonded to TII or Pb-II heavy-element centers are predicted to resonate at very high frequencies, up to 400 ppm for C-13 and over 1000 ppm for Si-29, outside the typical experimental NMR chemical-shift ranges for a given type of nuclei. The large C-13 and Si-29 NMR chemical shifts are ascribed to sizable relativistic spin-orbit effects, which can amount to more than 200 ppm for C-13 and more than 1000 ppm for Si-29, values unexpected for diamagnetic compounds of the main group elements. The origin of the vast spin-orbit contributions to the C-13 and Si-29 NMR shifts is traced to the highly efficient 6p -> 6p* metal-based orbital magnetic couplings and related to the 6p orbital-based bonding together with the low-energy gaps between the occupied and virtual orbital subspaces in the subvalent TII and Pb-II compounds. New NMR spectral regions for these compounds are suggested based on the fully relativistic density functional theory calculations in the Dirac-Coulomb framework carefully calibrated on the experimentally known NMR data for TII and Pb-II complexes.