Examining what happens when two closely related species come into secondary contact provides insight into the later stages of the speciation process. The Zosteropidae family of birds is one of the most rapidly speciating vertebrate lineages. Members of this family are highly vagile and geographically widespread, raising the question of how divergence can occur if populations can easily come into secondary contact. On the small island of Kolombangara, two closely related nonsister species of white‐eyes, Zosterops kulambangrae and Zosterops murphyi, are distributed along an elevational gradient and come into secondary contact at mid‐elevations. We captured 134 individuals of both species along two elevational transects. Using genotyping‐by‐sequencing data and a mitochondrial marker, we found no evidence of past hybridization events and strong persistence of species boundaries, even though the species have only been diverging for approximately 2 million years. We explore potential reproductive barriers that allow the two species to coexist in sympatry, including premating isolation based on divergence in plumage and song. We also conducted a literature review to determine the time it takes to evolve complete reproductive isolation in congeneric avian species/subspecies in secondary contact (restricted to cases where congeneric taxa are parapatric or have a hybrid zone), finding our study is one of the youngest examples of complete reproductive isolation studied in a genomic context reported in birds.