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 μ – τ sector constitute the most stringent limits up to date.