  Microquasars with high-mass companion stars are promising very-high-energy
(VHE; 0.1-100 TeV) gamma-ray emitters, but their behaviors above 10 TeV are
poorly known. Using the High Altitude Water Cherenkov (HAWC) observatory, we
search for excess gamma-ray emission coincident with the positions of known
high-mass microquasars (HMMQs). No significant emission is observed for LS
5039, Cygnus X-1, Cygnus X-3, and SS 433 with 1,523 days of HAWC data. We set
the most stringent limit above 10 TeV obtained to date on each individual
source. Under the assumption that HMMQs produce gamma rays via a common
mechanism, we have performed source-stacking searches, considering two
different scenarios: I) gamma-ray luminosity is a fraction $\epsilon_\gamma$ of
the microquasar jet luminosity, and II) very-high-energy gamma rays are
produced by relativistic electrons up-scattering the radiation field of the
companion star in a magnetic field $B$. We obtain $\epsilon_\gamma < 5.4\times
10^{-6}$ for scenario I, which tightly constrains models that suggest
observable high-energy neutrino emission by HMMQs. In the case of scenario II,
the non-detection of VHE gamma rays yields a strong magnetic field, which
challenges synchrotron radiation as the dominant mechanism of the microquasar
emission between 10 keV and 10 MeV.
