ABSTRACT We model the non-thermal emission spectrum of the extremely sub-Eddington X-ray binary system A0620-00. It is believed that this non-thermal emission is produced by radiatively inefficient ‘quiescent’ accretion on to a stellar-mass black hole present in the system. We post-process general relativistic magnetohydrodynamics (GRMHD) simulations with multiwavelength, fully polarized, relativistic radiative transfer calculations to predict broad-band spectra and emission polarization levels for a range of electron models and accretion rates. We find that a model with strong coupling of electrons and ions in the accretion disc and accretion rate of only $\dot{M}=3\times 10^{-13} \, \rm [M_⊙ \, yr^{-1}]$ is able to recover the observed X-ray spectral slope, as well as the excess of linear polarization detected in the source in the near-infrared (NIR)/optical bands. Our models constrain the spectral properties of a putative relativistic jet produced in this system. In addition, we show that the magnetized winds from our hot accretion flow carry away a small fraction of the orbital angular momentum of the binary, which is unable to explain the observed rapid orbital decay of the system. GRMHD simulations similar to the present ones are often used to explain emission from sub-Eddington supermassive black holes in Sgr A* or M87; the present simulations allow us to test whether some aspects of quiescent black hole accretion are scale-invariant.