Coevolution has long been thought to drive the exaggeration of traits, promote major evolutionary transitions such as the evolution of sexual reproduction and influence epidemiological dynamics. Despite coevolution's long suspected importance, we have yet to develop a quantitative understanding of its strength and prevalence because we lack generally applicable statistical methods that yield numerical estimates for coevolution's strength and significance in the wild. Here, we develop a novel method that derives maximum likelihood estimates for the strength of direct pairwise coevolution by coupling a well-established coevolutionary model to spatially structured phenotypic data. Applying our method to two well-studied interactions reveals evidence for coevolution in both systems. Broad application of this approach has the potential to further resolve long-standing evolutionary debates such as the role species interactions play in the evolution of sexual reproduction and the organisation of ecological communities.