The ordering properties of an anisotropic liquid crystal can be studied by recording C-13 NMR spectra at different temperatures for a number of rigid solutes. The traditional difficulty in analyzing C-13 data comes from the scarcity of experimental information about the carbon shielding tensors and from their limited transferability among different solutes. We show that these obstacles can be overcome by computing high-level ab initio shielding tensors, also including the solvent effects by the polarizable continuum model. The reliability of this combined approach is carefully verified, and the order parameters of several solutes are obtained by reanalyzing previously published spectra. The quality of the results is shown to be comparable to deuterium NMR without the need of isotopic substitution.