Recent work highlights that tens of Galactic double neutron stars are likely to be detectable in the millihertz band of the space-based gravitational-wave observatory, LISA, some of which might be detectable as radio pulsars using the Square Kilometer Array (SKA). We point out that the joint LISA + SKA detection of a fgw ≳ 1 mHz binary, corresponding to a binary period of ≲400 s, would enable precision measurements of ultrarelativistic phenomena. We show that, given plausible assumptions, multimessenger observations of ultrarelativistic binaries can be used to constrain the neutron star equation of state with remarkable fidelity. It may be possible to measure the mass–radius relation with a precision of ≈0.2 per cent after 10 yr of observations with the SKA. Such a measurement would be roughly an order of magnitude more precise than possible with other proposed observations. We summarize some of the other remarkable science made possible with multimessenger observations of millihertz binaries, and discuss the prospects for the detection of such objects.