Copenhagen has won praise from audiences and critics alike, as well as several prestigious awards. It also has gained the attention of academics. Jonothan Logan writes in American Scientist that, although he found the play to be "quick, clever and artfully plotted," he is concerned about Frayn's alteration of the historical facts and his rearrangement of "the moral landscape the real Bohr and Heisenberg inhabited." Logan contends that Frayn's reliance on Thomas Powers's book Heisenberg's War for the content of his play was faulty because the Powers book was flawed and thus "won little respect from historians."

Another scholar, Paul Lawrence Rose, writing for the Chronicle of Higher Education, begins his article: "Scholars are never satisfied when they see their specialized subjects turn fodder for stage, screen, or novels." Rose is a specialist on Heisenberg and he praises Frayn for developing "through his often electric dialogue...