  We compare different methods of computing the orbital eccentricity of
quasi-circular binary black hole systems using the orbital variables and
gravitational wave phase and frequency. For eccentricities of about a per cent,
most methods work satisfactorily. For small eccentricity, however, the
gravitational wave phase allows a particularly clean and reliable measurement
of the eccentricity. Furthermore, we measure the decay of the orbital
eccentricity during the inspiral and find reasonable agreement with
post-Newtonian results. Finally, we measure the periastron advance of
non-spinning binary black holes, and we compare them to post-Newtonian
approximations. With the low uncertainty in the measurement of the periastron
advance, we positively detect deviations between fully numerical simulations
and post-Newtonian calculations.
