  We present a method for the determination of upper limits on the transverse
velocity of the lensing galaxy in the quadruple quasar system Q2237+0305, based
on the lack of strong microlensing signatures in the quasar lightcurves. The
limits we derive here are based on four months of high quality monitoring data,
by comparing the low amplitudes of the lightcurves of the four components with
extensive numerical simulations. We make use of the absence of strong
variability of the components (especially components B and D) to infer that a
"flat" time interval of such a length is only compatible with an effective
transverse velocity of the lensing galaxy of v_bulk <=630 km/s for typical
microlenses masses of M_microlens=0.1 M_solar (or v_bulk <=2160 km/s for
M_microlens=1.0 M_solar) at the 90% confidence level. This method may be
applicable in the future to other systems.
