Markerless hand-tracking has become increasingly common on commercially available virtual and mixed reality headsets to improve the naturalness of interaction and immersivity of virtual environments. However, there has been limited examination of the performance of markerless hand-tracking on commercial head-mounted displays. Here, we propose an evaluation methodology that leverages a robotic manipulator to measure the positional accuracy, jitter, and latency of such systems and provides a standardized characterization framework of markerless hand-tracking. We apply this methodology to evaluate the hand-tracking performance of two recent mixed reality devices from Meta: the Quest Pro and Quest 3. Results demonstrate the influence of proximity to the headset, rotation of hand, and joint selected as the tracking feature on hand-tracking performance. We found that hand-tracking error and jitter were lowest for both headsets in conditions where the knuckle was the tracking point compared to the fingertip. Regarding positional accuracy, in best-performing conditions, the Quest Pro outperformed the Quest 3 with 1.22 cm of average error compared to 1.73 cm. The opposite result was true concerning jitter, with results of 1.77 cm and 1.11 cm for the Quest Pro and Quest 3, respectively. We found latency highly variable for the Quest Pro (15.8 - 229.2 ms) and Quest 3 (14.4 - 220.5 ms). This work provides a testing framework for highly systematic and repeatable performance measurements of markerless hand-tracking systems embedded in headsets.