  Non-standard interactions (NSIs) in the propagation of neutrinos in matter
can lead to significant deviations in neutrino oscillations expected within the
standard 3-neutrino framework. These additional interactions would result in an
anomalous flux of neutrinos observable at neutrino telescopes. The ANTARES
detector and its next-generation successor, KM3NeT, located in the abyss of the
Mediterranean Sea, have the potential to measure sub-dominant effects in
neutrino oscillations, coming from non-standard neutrino interactions. In this
contribution, a likelihood-based search for NSIs with 10 years of atmospheric
muon-neutrino data recorded with ANTARES is reported and sensitivity
projections for KM3NeT/ORCA, based on realistic detector simulations, are
shown. The bounds obtained with ANTARES in the NSI $\mu - \tau$ sector
constitute the most stringent limits up to date.
