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Just as a phylogeny encodes the evolutionary relationships among a group of organisms, a cophylogeny represents the coevolutionary relationships among symbiotic partners. Both are primarily reconstructed using computational analysis of biomolecular sequence data. The most widely used cophylogenetic reconstruction methods utilize an important simplifying assumption: species phylogenies for each set of coevolved taxa are required as input and assumed to be correct. Many studies have shown that this assumption is rarely – if ever – satisfied, and the consequences for cophylogenetic studies are poorly understood. To address this gap, we conduct a comprehensive performance study that quantifies the relationship between species tree estimation error and downstream cophylogenetic estimation accuracy. We study the performance of state-of-the-art methods for cophylogenetic reconstruction using in silico model-based simulations. Our investigation also assessed cophylogenetic reproducibility using genomic sequence data from two important models of symbiosis: soil-associated fungi and their endosymbiotic bacteria, and bobtail squid and their bioluminescent bacterial symbionts. Our findings conclusively demonstrate the major impact that upstream phylogenetic estimation error has on downstream cophylogenetic reconstruction. Relative to other experimental factors such as cophylogenetic estimation method choice and coevolutionary event costs, phylogenetic estimation error ranked highest in importance based on a random forest-based variable importance assessment. We conclude with practical guidance and future research directions. Among the many considerations needed for accurate cophylogenetic reconstruction – choice of computational method, method settings, sampling design, and others – just as much attention must be paid to careful species phylogeny estimation using modern best practices.