Calculations of the nuclear magnetic resonance chemical-shielding tensors of a suite of mercury-containing materials using various cluster models for the structures provide a stringent test of the procedures for forming models and for calculation with various methods. The inclusion of higher co-ordination shells in the molecular clusters permits quantum chemical calculations of Hg-199 chemical-shielding tensor elements within 3% of the experimental values. We show that it is possible to reduce the size of computationally expensive molecular-cluster calculations with limited effect on calculated NMR parameters by carefully introducing the frozen core approximation. The importance of the relativistic Hamiltonian for accurate predictions of chemical-shielding values is demonstrated within the molecular cluster approach. The results demonstrate that careful design of a cluster to represent the solid-state structure, inclusion of relativistic components in the Hamiltonian at least at the spin-orbit level, and judicious use of approximations are essential to obtain good agreement with experimental results.