The evolution of proteins cannot be fully understood without taking into account the coevolutionary linkages entangling them. From a practical point of view, coevolution between protein families has been used as a way of detecting protein interactions and functional relationships from genomic information. The most common approach to inferring protein coevolution involves the quantification of phylogenetic tree similarity using a family of methodologies termed mirrortree. In spite of their success, a fundamental problem of these approaches is the lack of an adequate statistical framework to assess the significance of a given coevolutionary score (tree similarity). As a consequence, a number of ad hoc filters and arbitrary thresholds are required in an attempt to obtain a final set of confident coevolutionary signals.