Toward an understanding of the factors that affect the chemical shift in the Xe nuclear magnetic resonance spectrum of Xe atoms trapped in cages which may have applications as biosensors, we carry out calculations of Xe nuclear magnetic shielding using Hartree-Fock and density functional methods. The resulting values for various Xe positions within the cage can be described by an analytical function of Xe and cage atom coordinates. This shielding function is used in Monte Carlo canonical averaging of a Xe atom within cryptophane cages to investigate the dependence of the Xe chemical shifts on cage size (cryptophane-A versus cryptophane-E), isotopic substitution, and temperature. We compare our theoretical average Xe chemical shifts with the experimental values in four types of cryptophane cages, and with the temperature and isotopic dependence of Xe chemical shifts in cryptophane-A, and achieve a quantitative understanding of the factors that influence the Xe chemical shifts in these cages. The predicted effects on the Xe chemical shifts of mechanical distortion of the cryptophane-A cage provide some insight into the applications of Xe in cages as biosensors. (C) 2003 American Institute of Physics.