Previous work by Motch et al. suggested that in the low/hard state of GX 339-4 the soft X-ray power law extrapolated backward in energy agrees with the IR flux level. Corbel & Fender later showed that the typical hard-state radio power law extrapolated forward in energy meets the backward-extrapolated X-ray power law at an IR spectral break, which was explicitly observed twice in GX 339-4. This IR coincidence has been cited as further evidence that synchrotron radiation from a jet might make a significant contribution to the observed X-rays in hard-state black hole systems. We quantitatively explore this hypothesis with a series of simultaneous radio/X-ray observations of GX 339-4, taken during its 1997, 1999, and 2002 hard states. We fit these spectra, in detector space, with a simple, but remarkably successful, doubly broken power-law model that indeed requires an IR spectral break. For these observations, the break position and the integrated radio/IR flux have stronger dependences upon the X-ray flux than the simplest jet model predictions. If one allows for a softening of the X-ray power law with increasing flux, then the jet model can agree with the observed correlation. We also find evidence that the radio flux-X-ray flux correlation previously observed in the 1997 and 1999 GX 339-4 hard states shows a parallel track for the 2002 hard state. The slope of the 2002 correlation is consistent with observations taken in prior hard states; however, the radio amplitude is reduced. We then examine the radio flux-X-ray flux correlation in Cyg X-1 through the use of 15 GHz radio data obtained with the Ryle radio telescope and Rossi X-Ray Timing Explorer data from the All-Sky Monitor and pointed observations. We again find evidence of parallel tracks, and here they are associated with "failed transitions," or the beginning of a transition, to the soft state. We also find that for Cyg X-1 the radio flux is more fundamentally correlated with the hard, rather than the soft, X-ray flux.