  Gravitational-wave (GW) astronomy is transforming our understanding of the
Universe by probing phenomena invisible to electromagnetic observatories. A
comprehensive exploration of the GW frequency spectrum is essential to fully
harness this potential. Remarkably, current methods have left the $\mu$Hz
frequency band almost untouched. Here, we show that this $\mu$Hz gap can be
filled by searching for deviations in the orbits of binary systems caused by
their resonant interaction with GWs. In particular, we show that laser ranging
of the Moon and artificial satellites around the Earth, as well as timing of
binary pulsars, may discover the first GW signals in this band, or otherwise
set stringent new constraints. To illustrate the discovery potential of these
binary resonance searches, we consider the GW signal from a cosmological
first-order phase transition, showing that our methods will probe models of the
early Universe that are inaccessible to any other near-future GW mission. We
also discuss how our methods can shed light on the possible GW signal detected
by NANOGrav, either constraining its spectral properties or even giving an
independent confirmation.
