  Runaway stars form bow shocks by ploughing through the interstellar medium at
supersonic speeds and are promising sources of non-thermal emission of photons.
One of these objects has been found to emit non-thermal radiation in the radio
band. This triggered the development of theoretical models predicting
non-thermal photons from radio up to very-high-energy (VHE, E $\geq 0.1$TeV)
gamma rays. Subsequently, one bow shock was also detected in X-ray
observations. However, the data did not allow discrimination between a hot
thermal and a non-thermal origin. Further observations of different candidates
at X-ray energies showed no evidence for emission at the position of the bow
shocks either. A systematic search in the \textit{Fermi}-LAT energy regime
resulted in flux upper limits for 27 candidates listed in the E-BOSS catalogue.
Here we perform the first systematic search for VHE gamma-ray emission from bow
shocks of runaway stars. Using all available archival H.E.S.S. data we search
for very-high-energy gamma-ray emission at the positions of bow shock
candidates listed in the second E-BOSS catalogue release. Out of the 73 bow
shock candidates in this catalogue, 32 have been observed with H.E.S.S. None of
the observed 32 bow shock candidates in this population study show significant
emission in the H.E.S.S. energy range. Therefore, flux upper limits are
calculated in five energy bins and the fraction of the kinetic wind power that
is converted into VHE gamma rays is constrained. Emission from stellar bow
shocks is not detected in the energy range between 0.14 and 18 TeV. The
resulting upper limits constrain the level of VHE gamma-ray emission from these
objects down to 0.1-1 % of the kinetic wind energy.
