A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) of a set of testimonies implies a higher probability that the witnesses are reliable. Recently, it has been proved that the Shogenji measure of coherence is reliability conducive in restricted scenarios (e.g., Olsson and Schubert, Synthese, 157:297–308, 2007). In this article, I investigate whether the Shogenji measure, or any other coherence measure, is reliability conducive in general. An impossibility theorem is proved to the effect that this is not the case. I conclude that coherence is not reliability conducive.