A major issue in the control of malaria is the evolution of drug resistance. Ecological theory has demonstrated that pathogen superinfection and the resulting within-host competition influences the evolution of specific traits. Individuals infected with Plasmodium falciparum are consistently infected by multiple parasites; however, while this probably alters the dynamics of resistance evolution, there are few robust mathematical models examining this issue. We developed a general theory for modelling the evolution of resistance with host superinfection and examine: (i) the effect of transmission intensity on the rate of resistance evolution; (ii) the importance of different biological costs of resistance; and (iii) the best measure of the frequency of resistance. We find that within-host competition retards the ability and slows the rate at which drug-resistant parasites invade, particularly as the transmission rate increases. We also find that biological costs of resistance that reduce transmission are less important than reductions in the duration of drug-resistant infections. Lastly, we find that random sampling of the population for resistant parasites is likely to significantly underestimate the frequency of resistance. Considering superinfection in mathematical models of antimalarial drug resistance may thus be important for generating accurate predictions of interventions to contain resistance.