We use the Binary Population and Spectral Synthesis models to test the recent suggestion that red supergiants can provide an accurate age estimate of a coeval stellar population that is unaffected by interacting binary stars. Ages are estimated by using both the minimum luminosity of red supergiants and the mean luminosity of red supergiants in a cluster. We test these methods on a number of observed star clusters and find our results in agreement with previous estimates. Importantly, we find the difference between the ages derived from stellar population models with and without a realistic population of interacting binary stars is only a few hundred thousand years at most. We find that the mean luminosity of red supergiants in a cluster is the best method to determine the age of a cluster because it is based on the entire red supergiant population rather than using only the least luminous red supergiant.