The family Melampittidae is endemic to New Guinea and consists of two monotypic genera: Melampitta lugubris (Lesser Melampitta) and Megalampitta gigantea (Greater Melampitta). Both Melampitta species have scattered and disconnected distributions across New Guinea in the central mountain range and in some of the outlying ranges. While M. lugubris is common and found in most montane regions of the island, M. gigantaea is elusive and known from only six localities in isolated pockets on New Guinea with very specific habitats of limestone and sinkholes. In this project, we apply museomics to determine the population structure and demographic history of these two species. We re-sequenced the genomes of all seven known M. gigantaea samples housed in museum collections as well as 24 M. lugubris samples from across its distribution. By comparing population structure between the two species, we investigate to what extent habitat dependence, such as in M. gigantaea, may affect population connectivity. Phylogenetic and population genomic analyses, as well as acoustic variation revealed that M. gigantaea consists of a single population in contrast to M. lugubris that shows much stronger population structure across the island. We suggest a recent collapse of M. gigantaea into its fragmented habitats as an explanation to its unexpected low diversity and lack of population structure. The deep genetic divergences between the M. lugubris populations on the Vogelkop region, in the western central range and the eastern central range, respectively, suggests that these three populations should be elevated to full species level. This work sheds new light on the mechanisms that have shaped the intriguing distribution of the two species within this family and is a prime example of the importance of museum collections for genomic studies of poorly known and rare species.