Ring currents can exert a large effect upon the chemical shielding of NMR resonances. The analytical expression developed by Waugh and Fessenden (Waugh, J. S.; Fessenden, R. W. J. Am. Chem. Soc. 1957, 79, 846) and Johnson and Bovey (Johnson, C. E.; Bovey, F. A. J. Chem. Phys. 1957, 29, 1012) only quantifies the contribution of ring currents to the isotropic component of the shielding tensor. In the work described here an additional analytical expression is developed so that the contribution of ring currents to the full shielding tensor can be calculated, allowing an estimate of the influence of ring currents upon the chemical shielding anisotropy (CSA, Δσ). To test that this pair of analytical expressions can provide a reasonable estimate of the contribution of ring currents to the full shielding tensor a series of density functional calculations (DFT) were carried out. A shielding tensor in a model compound was calculated in two distinct ways. For the first series, DFT shielding calculations of the model compound were carried out in the presence of a benzene ring. For the second series a ring current contribution to the shielding tensor was calculated via the new expressions, and this was added to the result of a DFT shielding calculation which used in place of benzene the nonaromatic analogue 1,3 cyclohexadiene. The two series of results proved to be in excellent agreement. The pair of analytical expressions are used to calculate ring current contributions to the CSA (Δσ) of ¹H^N backbone amide resonances in a structure of the second type 2 module from the protein fibronectin. Significant CSA variations are predicted in particular for the ¹H^N of G42 which is most likely involved in a N-H⋯π aromatic hydrogen bond.