  Multiwavelength radiation from relativistic particles accelerated at shocks
in novae and other astrophysical sources carries a wealth of information about
the outflow properties and the microphysical processes at work near the shocks.
The observation of GeV gamma-rays from novae by Fermi/LAT demonstrates that the
shocks in these systems can accelerate particles to energies of at least $\sim
10$ GeV. The low-energy extension of the same non-thermal particle distribution
inevitably gives rise to emission extending into the X-ray band. Above $\gtrsim
10$ keV this radiation can escape the system without significant
absorption/attenuation, and can potentially be detected by NuSTAR. We present
theoretical models for hard X-ray and gamma-ray emission from radiative shocks
in both leptonic and hadronic scenarios, accounting for the rapid evolution of
the downstream properties due to the fast cooling of thermal plasma. Due to
strong Coulomb cooling of the mildly relativistic electrons nominally
responsible for producing hard X-ray emission, only a fraction of $10^{-4} -
10^{-3}$ of the gamma-ray luminosity is radiated in the NuSTAR band;
nevertheless, this emission could be detectable simultaneous with the LAT
emission in bright gamma-ray novae with a $\sim 50$ ks exposure. Our work
demonstrates how combined hard X-ray and gamma-ray observations can be used to
constrain properties of the nova outflow (velocity, density and mass outflow
rate) and particle acceleration at the shock. A very low X-ray to gamma-ray
luminosity ratio ($L_{\rm X}/L_{\gamma} \lesssim 5 \times 10^{-4}$) would
disfavor leptonic models for the gamma-ray emission. Our model can also be
applied to other astrophysical environments with radiative shocks, including
Type IIn supernovae and colliding winds in massive star binaries.
