  Runaway stars form bow shocks by sweeping up interstellar matter in their
direction of motion. Theoretical models predict a spectrally wide non-thermal
component reaching up to gamma-ray energies at a flux level detectable with
current instruments. They were motivated by a detection of non-thermal radio
emission from the bow shock of BD$+43^\circ3654$ and a possible detection of
non-thermal X-rays from AE Aurigae. A search in the high-energy regime using
data from \textit{Fermi}-LAT resulted in flux upper limits for 27 candidates
listed in the first E-BOSS catalogue. We perform the first systematic search
for TeV emission from bow shocks of runaway stars. Using all available archival
H.E.S.S. I data we search for very-high-energy gamma-ray emission at the
positions of bow shock candidates listed in the second E-BOSS catalogue. This
catalogue comprises 73 bow shock candidates, 32 of which have been observed
with the H.E.S.S. telescopes. None of the observed bow shock candidates shows
significant emission in the H.E.S.S. energy range. The resulting upper limits
are used to constrain current models for non-thermal emission from these
objects.
