  ANTARES is the largest high-energy neutrino telescope in the Northern
Hemisphere. This contribution presents the results of a search, based on the
ANTARES data collected over 17 months between November 2014 and April 2016, for
high energy neutrino emission in coincidence with TeV $\gamma$-ray flares from
Markarian 421 and Markarian 501, two bright BL Lac extragalactic sources highly
variable in flux, detected by the HAWC observatory. The analysis is based on an
unbinned likelihood-ratio maximization method. The $\gamma$-ray lightcurves
(LC) for each source were used to search for temporally correlated neutrinos,
that would be produced in pp or p-$\gamma$ interactions. The impact of
different flare selection criteria on the discovery neutrino flux is discussed.
Plausible neutrino spectra derived from the observed $\gamma$-ray spectra in
addition to generic spectra $E^{-2}$ and $E^{-2.5}$ are tested.
