  We describe a fast, approximate method to characterize the orbits of
satellites around a central binary in numerical simulations. A goal is to
distinguish the free eccentricity -- random motion of a satellite relative to a
dynamically cool orbit -- from oscillatory modes driven by the central binary's
time-varying gravitational potential. We assess the performance of the method
using the Kepler-16, Kepler-47, and Pluto-Charon systems. We then apply the
method to a simulation of orbital damping in a circumbinary environment,
resolving relative speeds between small bodies that are slow enough to promote
mergers and growth. These results illustrate how dynamical cooling can set the
stage for the formation of Tatooine-like planets around stellar binaries and
the small moons around the Pluto-Charon binary planet.
