Using accurate and fully general-relativistic simulations we assess the effect that magnetic fields have on the gravitational-wave emission produced during the inspiral and merger of magnetized neutron stars. In particular, we show that magnetic fields have an impact after the merger, because they are amplified by a Kelvin–Helmholtz instability, but also during the inspiral, most likely because the magnetic tension reduces the stellar tidal deformation for extremely large initial magnetic fields, B0≳ 1017 G. We quantify the influence of magnetic fields by computing the overlap, , between the waveforms produced during the inspiral by magnetized and unmagnetized binaries. We find that for any realistic magnetic field strength B0≲ 1014 G the overlap during the inspiral is and is quite insensitive to the mass of the neutron stars. Only for unrealistically large magnetic fields like B0≃ 1017 G the overlap does decrease noticeably, becoming at our resolutions for stars with baryon masses Mb≃ 1.4/1.6 M⊙, respectively. Because neutron stars are expected to merge with magnetic fields ∼108–1010 G and because present detectors are sensitive to , we conclude that it is very unlikely that the present detectors will be able to discern the presence of magnetic fields during the inspiral of neutron stars.