Neutrino Non-Standard Interactions appear naturally in several extensions of the Standard Model which try to accommodate mechanisms for the origin of neutrino masses. The Non-Standard Interactions are incorporated through effective four-fermion interactions which lead to both charged-current and neutral-current interactions. The latter affect coherent forward scattering of neutrinos on fermions in matter, ultimately leading to modifications of the oscillation probabilities of neutrinos experiencing matter potentials. Therefore, strong matter effects influencing the core-crossing trajectories of atmospheric neutrinos traversing the Earth would enhance such modifications, making neutrino telescopes ideal candidates for Non-Standard Interactions studies. This work presents the results of the Non-Standard Interactions search with the KM3NeT/ORCA6 and ANTARES neutrino telescopes, reporting bounds to the interaction coupling strengths at 90% CL which are comparable to the current most stringent limits in both cases.