Humans rely on ankle torque to maintain standing balance, particularly in the presence of small to moderate perturbations. Reductions in maximum torque (MT) production and maximum rate of torque development (MRTD) occur at the ankle with age, diminishing stability. Ankle exoskeletons are powered orthotic devices that may assist older adults by compensating for reduced muscle force and power production capabilities. They may also be able to assist with ankle strategies used for balance. However, no studies have investigated the effect of such devices on balance in older adults. Here, we model the effect ankle exoskeletons have on stability in physics-based models of healthy young and old adults, focusing on the mitigation of age-related deficits such as reduced MT and MRTD. We show that an ankle exoskeleton moderately reduces feasible stability boundaries in users who have full ankle strength. For individuals with age-related deficits, there is a trade-off. While exoskeletons augment stability in low velocity conditions, they reduce stability in some high velocity conditions. Our results suggest that well-established control strategies must still be experimentally validated in older adults.