In malaria-endemic countries, the limited availability of affordable antimalarial medication has contributed to the widespread distribution of inferior counterfeit drugs. We study such markets to determine how philanthropic donors can best allocate limited funds to subsidize the purchase or sales of antimalarial drugs via private-sector distribution channels. We also consider the potential effectiveness of other interventions to improve outcomes in the presence of counterfeit drugs. To examine the supply chain of antimalarials, we develop a game-theoretic model in which the retailer has a strategic choice to source legitimate drugs from a certified supplier, potentially counterfeit drugs from an uncertified supplier, or both. In contrast with the extant literature, we show that in the presence of counterfeits, employing a purchase subsidy alone may no longer be optimal. In particular, when the donor's budget is small, the donor may prefer to offer a sales subsidy that covers both legitimate and counterfeit drugs; moreover, if the drug's retail price is exogenous and demand uncertainty is high, the donor may need to refrain from offering any subsidy at all. We also evaluate five strategies that have been employed to combat counterfeit drugs (improving consumer awareness, increasing the cost of sourcing counterfeits, adopting traceability technology, cracking down on the supply, and imposing price controls) and identify the conditions under which these approaches can either improve or worsen outcomes. Finally, we perform an extensive numerical analysis, calibrating the models to malaria data from Mozambique. Our paper provides guidance as to how to improve outcomes in the presence of counterfeit drugs. Specifically, our results indicate the need for regulators and donors to understand specific market characteristics (e.g., retailers' pricing power and demand uncertainty) in order to design effective subsidy schemes and select appropriate technologies and policies to improve access to life-saving medicines.