X-ray and radio data recently acquired as part of a project to study Cyg OB2#9 are used to constrain physical models of the binary system, providing in-depth knowledge about the wind-wind collision and the thermal, and non-thermal, emission arising from the shocks. We use a three-dimensional, adaptive mesh refinement simulation (including wind acceleration, radiative cooling, and the orbital motion of the stars) to model the gas dynamics of the wind-wind collision. The simulation output is used as the basis for radiative transfer calculations considering the thermal X-ray emission and the thermal/non-thermal radio emission. To obtain good agreement with the X-ray observations, our initial mass-loss rate estimates require a down-shift by a factor of roughly 7.7 to $6.5times10^{-7}$ and $7.5times10^{-7}$ solar mass per year for the primary and secondary star, respectively. Furthermore, the low gas densities and high shock velocities in Cyg OB2#9 are suggestive of unequal electron and ion temperatures, and the X-ray analysis indicates that an (immediately post-shock) electron-ion temperature ratio of $simeq 0.1$ is also required. The radio emission is dominated by (non-thermal) synchrotron emission. A parameter space exploration provides evidence against models assuming equipartition between magnetic and relativistic energy densities. However, fits of comparable quality can be attained with models having stark contrasts in the ratio of magnetic-to-relativistic energy densities. The radio models also reveal a subtle effect whereby inverse Compton cooling leads to an increase in emissivity as a result of the synchrotron characteristic frequency being significantly reduced. Finally, using the results of the radio analysis, we estimate the surface magnetic field strengths to be $approx 0.3-52;$G. (Abridged)
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