Plant-based repellents represent a safe, economic, and viable alternative to managing invasive insects that threaten native fauna. Observations of self-medication in animals can provide important cues to the medicinal properties of plants. A recent study in the Galapagos Islands found that Darwin’s finches apply the leaves of Psidium galapageium (Hooker 1847) to their feathers, extracts of which were repellent to mosquitoes and the parasitic fly Philornis downsi (Dodge & Aitkens 1968; Diptera: Muscidae). Introduced mosquitoes are suspected vectors of avian pathogens in the Galapagos Islands, whereas the larvae of P. downsi are blood-feeders, causing significant declines of the endemic avifauna. In this study, we investigated the volatile compounds found in P. galapageium, testing each against a model organism, the mosquito Anopheles arabiensis (Patton 1905; Diptera: Culicidae), with the aim of singling out the most effective compound for repelling dipterans. Examinations of an ethanolic extract of P. galapageium, its essential oil and each of their respective fractions, revealed a mixture of monoterpenes and sesquiterpenes, the latter consisting mainly of guaiol, trans-nerolidol, and β-eudesmol. Of these, trans-nerolidol was identified as the most effective repellent to mosquitoes. This was subsequently tested at four different concentrations against P. downsi, but we did not find a repellence response. A tendency to avoid the compound was observed, albeit significance was not achieved in any case. The lack of repellence suggests that flies may respond to a combination of the volatile compounds found in P. galapageium, rather than to a single compound.