  Gravitational microlensing offers a powerful method with which to probe a
variety of binary-lens systems, as the binarity of the lens introduces
deviations from the typical (single-lens) Paczy\'nski behaviour in the event
light curves. Generally, a static binary lens is considered to fit the observed
light curve and, when the orbital motion is taken into account, an
oversimplified model is usually employed. In this paper, we treat the
binary-lens motion in a realistic way and focus on simulated events that are
fitted well by a Paczy\'nski curve. We show that an accurate timing analysis of
the residuals (calculated with respect to the best-fitting Paczy\'nski model)
is usually sufficient to infer the orbital period of the binary lens. It goes
without saying that the independently estimated period may be used to further
constrain the orbital parameters obtained by the best-fitting procedure, which
often gives degenerate solutions. We also present a preliminary analysis of the
event OGLE-2011-BLG-1127 / MOA-2011-BLG-322, which has been recognized to be
the result of a binary lens. The period analysis results in a periodicity of
\simeq 12 days, which confirms the oscillation of the observed data around the
best-fitting model. The estimated periodicity is probably associated with an
intrinsic variability of the source star, and therefore there is an opportunity
to use this technique to investigate either the intrinsic variability of the
source or the effects induced by the binary-lens orbital motion.
