In this work, the role of swing limb dynamics in the stabilization of legged systems is investigated. To quantify the contribution of arm swing during whole-body balancing, the balancing capability of a bipedal robotic platform is evaluated computationally during single and double foot contact for two configurations: arms fixed and arms free to move. The balancing capability with each arm configuration is evaluated by constructing its corresponding balance stability boundary, a threshold between balanced and falling states that includes all possible center of mass (COM) states that are balanced with respect to the specified arm and foot contact configuration. In this analysis, the bipedal robotic platform is modeled as a kinematic tree structure with floating-base dynamics in the sagittal plane. In addition to floating-base and joint-space dynamics, the complete COM-space dynamics of the system is established, including the formulation of the angular momentum (and its rate) of each rigid link, as well as a model of actuation dynamics based on motor characteristics. The comparison of the two balance stability regions yields both a quantitative measure of the enhancement in total balance capability and qualitative insights into the mechanism by which arm swing leads to enhanced capability. The role of arm swing angular momentum is also analyzed from the robot’s experimental gait trajectories as a potential means of benchmarking controller performance.