We present a solid-state NMR study of H2 molecules confined inside the cavity of C70 fullerene cages over a wide range of temperatures (300 K to 4 K). The proton NMR spectra are consistent with a model in which the dipole–dipole coupling between the ortho-H2 protons is averaged over the rotational/translational states of the confined quantum rotor, with an additional chemical shift anisotropy δHCSA=10.1 ppm induced by the carbon cage. The magnitude of the chemical shift anisotropy is consistent with DFT estimates of the chemical shielding tensor field within the cage. The experimental NMR data indicate that the ground state of endohedral ortho-H2 in C70 is doubly degenerate and polarized transverse to the principal axis of the cage. The NMR spectra indicate significant magnetic alignment of the C70 long axes along the magnetic field, at temperatures below ∼10 K.