New gas-phase NMR measurements of the shielding constants of Si-29, Ge-73, and H-1 nuclei in SiH4 and GeH4 are reported. The results, extrapolated to zero density, provide accurate isolated molecule values, best suited for comparison with theoretical calculations. Using the recent ab initio results for these molecules and the measured chemical shifts, we determine the absolute shielding scales for Si-29 and Ge-73. This allows us to provide new values of the nuclear magnetic dipole moments for these two nuclei; in addition, we examine the dipole moments of C-13 and Sn-119.