  Microquasars are potential $\gamma$-ray emitters. Indications of transient
episodes of $\gamma$-ray emission were recently reported in at least two
systems: Cyg X-1 and Cyg X-3. The identification of additional
$\gamma$-ray-emitting microquasars is required to better understand how
$\gamma$-ray emission can be produced in these systems. Theoretical models have
predicted very high-energy (VHE) $\gamma$-ray emission from microquasars during
periods of transient outburst. Observations reported herein were undertaken
with the objective of observing a broadband flaring event in the $\gamma$-ray
and X-ray bands. Contemporaneous observations of three microquasars, GRS
1915+105, Circinus X-1, and V4641 Sgr, were obtained using the High Energy
Spectroscopic System (H.E.S.S.) telescope array and the Rossi X-ray Timing
Explorer (RXTE) satellite. X-ray analyses for each microquasar were performed
and VHE $\gamma$-ray upper limits from contemporaneous H.E.S.S. observations
were derived. No significant $\gamma$-ray signal has been detected in any of
the three systems. The integral $\gamma$-ray photon flux at the observational
epochs is constrained to be $I(> 560 {\rm\ GeV}) < 7.3\times10^{-13}$ cm$^{-2}$
s$^{-1}$, $I(> 560 {\rm\ GeV}) < 1.2\times10^{-12}$ cm$^{-2}$ s$^{-1}$, and
$I(> 240 {\rm\ GeV}) < 4.5\times10^{-12}$ cm$^{-2}$ s$^{-1}$ for GRS 1915+105,
Circinus X-1, and V4641 Sgr, respectively. The $\gamma$-ray upper limits
obtained using H.E.S.S. are examined in the context of previous Cherenkov
telescope observations of microquasars. The effect of intrinsic absorption is
modelled for each target and found to have negligible impact on the flux of
escaping $\gamma$-rays. When combined with the X-ray behaviour observed using
RXTE, the derived results indicate that if detectable VHE $\gamma$-ray emission
from microquasars is commonplace, then it is likely to be highly transient.
