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Abstract The performance of optimally tuned range‐separated hybrid (OT‐RSH) functional calculations in predicting accurate isotropic nuclear magnetic shielding (σ) and chemical shift values is examined. To that end, the results of OT‐RSH and other approximate density functional theory calculations are assessed against recently published benchmark CCSD(T) calculations for a test set consisting of several molecules and bond types. It is found that for atoms in single bonds with a large paramagnetic contribution to σ, OT‐RSH offers a significant improvement in prediction of shielding constants over popular semi‐local and hybrid density functionals, yielding non‐empirical results that are as accurate as those of semi‐empirical density functionals often used for prediction of shielding constants. This success is attributed to the improved fundamental gap prediction of the OT‐RSH approach. For atoms in multiple bonds, however, larger errors often persist. By comparing OT‐RSH and recently reported double‐hybrid functional results, the remaining difficulties are traced to significant non‐local correlation.