Strong evidence against Penrose's conclusion would necessarily have to be strong (or at least moderate) counterarguments to each of the weak arguments which support his position; it appears to me that faith in reductionism and an observation of an algorithmic consciousness qualify as strong counterarguments, and I think that there's a very high probability that Tegmark's work showing that the brain mechanisms that we know about function well in classical physics qualifies as a moderate counterargument to the key points. (This would become strong if combined with proof that what we know is sufficient to model consciousness.)

The evolutionary counterargument (it is unlikely that small changes iterating over time would result in quantum behavior, even if quantum behavior were useful) I reject as false, because evolutionary processes aren't goal-oriented and aren't smart enough to avoid using quantum behavior.