  We present a theory of nuclear magnetic resonance (NMR) shielding tensors for
electronic states with arbitrary degeneracy. The shieldings are here expressed
in terms of generalized Zeeman ($g^{(k)}$) and hyperfine ($A^{(k)}$) tensors,
of all ranks $k$ allowed by the size of degeneracy. Contrary to recent
proposals [T. O. Pennanen and J. Vaara, Phys. Rev. Lett. 100, 133002 (2008)],
our theory is valid in the strong spin-orbit coupling limit. Ab initio
calculations for the 4-fold degenerate $\Gamma_8$ ground state of
lanthanide-doped fluorite crystals CaF$_2$:Ln (Ln = Pr$^{2+}$, Nd$^{3+}$,
Sm$^{3+}$, and Dy$^{3+}$) show that previously neglected contributions can
account for more than 50% of the paramagnetic shift.
