  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. Kyutoku and Nishino point out that some of these binaries
might be detectable as radio pulsars using the Square Kilometer Array (SKA). We
point out that the joint LISA+SKA detection of a $f_\text{gw}\gtrsim$1 mHz
binary, corresponding to a binary period of $\lesssim$400 s, would enable
precision measurements of ultra-relativistic phenomena. We show that, given
plausible assumptions, multi-messenger observations of ultra-relativistic
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 $\approx$0.2% 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 multi-messenger observations of
millihertz binaries, and discuss the prospects for the detection of such
objects.
