Natural history collections are increasingly valued as genomic resources. Their specimens reflect the combined efforts of collectors and curators over hundreds of years. For many rare or endangered species, specimens are the only readily available source of DNA. We leveraged specimens from a historical collection to study the evolutionary history of wood-partridges in the genus Dendrortyx. The three Dendrortyx species are found in the highlands of central Mexico and Central America south to Costa Rica. One of these species is endangered, and in general, Dendrortyx are secretive and poorly represented in tissue collections. We extracted DNA from historical museum specimens and sequenced ultraconserved elements (UCEs) and mitochondrial DNA (mtDNA) to assess their phylogeny and divergence times. Phylogenies built from hundreds to thousands of nuclear markers were well resolved and largely congruent with an mtDNA phylogeny. The divergence times revealed an unusually old avian divergence across the Isthmus of Tehuantepec in the Pliocene around 3.6 million years ago. Combined with other recent studies, our results challenge the general pattern that highland bird divergences in Mesoamerica are relatively young and influenced by the Pleistocene glacial cycles compared to the older divergences of reptiles and plants, which are thought to overlap more with periods of mountain formation. We also found evidence for monophyletic genetic lineages in mountain ranges within the widespread D. macroura, which should be investigated further with integrative taxonomic methods. Our study demonstrates the power of museum genomics to provide insight into the evolutionary histories of groups where modern samples are lacking.