The self-assembled supramolecular host [Ga(4)L6](12-)(1; L = 1,5-bis[2,3-dihydroxybenzamido]naphthalene) can encapsulate cationic guest molecules within its hydrophobic cavity and catalyze the chemical transformations of bound guests. The cavity of host 1 is lined with aromatic naphthalene groups, which create a magnetically shielded interior environment, resulting in upfield shifted (1-3 ppm) NMR resonances for encapsulated guest molecules. Using gauge independent atomic orbital (GIAO) DFT computations, we show that H-1 NMR chemical shifts for guests encapsulated in 1 can be efficiently and accurately calculated and that valuable structural information is obtained by comparing calculated and experimental chemical shifts. The H-1 NMR chemical shift calculations are used to map the magnetic environment of the interior of 1, discriminate between different host-guest geometries, and explain the unexpected downfield chemical shift observed for a particular guest molecule interacting with host 1.