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Molecular motors are nanoscale systems that convert chemical free energy to directed motion or work. We use molecular simulation to examine a family of catenane molecular motors and to analyze their performance compared to the physical limit provided by thermodynamic uncertainty relations (TURs). By varying the pair potentials and designs of the catenane motors, we find that the precision of the molecular motor currents can vary over orders of magnitude, but that precision is always observed to be far lower than the TUR limit. We further quantitatively rationalize the deviation from the TUR bound, illustrating that we can anticipate the degree to which a motor fails to saturate the TUR in terms of four physical parameters: the chemical potential driving the motor, the rate of fuel decomposition, the coupling between fuel decomposition and motor motion, and the rate of undriven motor motion. The analysis suggests that, for the catenane motors to become appreciably more efficient with respect to the TUR, it will be necessary to (i) make the fueling reaction less exergonic and (ii) couple the consumption of fuel more tightly to biased motion.