Cophylogeny is the congruence of phylogenetic relationships between two different groups of organisms due to their long‐term interaction. We investigated the use of tree shape distance measures to quantify the degree of cophylogeny. We implemented a reverse‐time simulation model of pathogen phylogenies within a fixed host tree, given cospeciation probability, host switching, and pathogen speciation rates. We used this model to evaluate 18 distance measures between host and pathogen trees including two kernel distances that we developed for labeled and unlabeled trees, which use branch lengths and accommodate different size trees. Finally, we used these measures to revisit published cophylogenetic studies, where authors described the observed associations as representing a high or low degree of cophylogeny. Our simulations demonstrated that some measures are more informative than others with respect to specific coevolution parameters especially when these did not assume extreme values. For real datasets, trees’ associations projection revealed clustering of high concordance studies suggesting that investigators are describing it in a consistent way. Our results support the hypothesis that measures can be useful for quantifying cophylogeny. This motivates their usage in the field of coevolution and supports the development of simulation‐based methods, i.e., approximate Bayesian computation, to estimate the underlying coevolutionary parameters.