Conjugative plasmids are mobile elements that spread horizontally between bacterial hosts and often confer adaptive phenotypes, including antimicrobial resistance (AMR). Theory suggests that opportunities for horizontal transmission favor plasmids with higher transfer rates, whereas selection for plasmid carriage favors less-mobile plasmids. However, little is known about the mechanisms leading to variation in transmission rates in natural plasmids or the resultant effects on their bacterial host. We investigated the evolution of AMR plasmids confronted with different immigration rates of susceptible hosts. Plasmid RP4 did not evolve in response to the manipulations, but plasmid R1 rapidly evolved up to 1,000-fold increased transfer rates in the presence of susceptible hosts. Most evolved plasmids also conferred on their hosts the ability to grow at high concentrations of antibiotics. This was because plasmids evolved greater copy numbers as a function of mutations in the copA gene controlling plasmid replication, causing both higher transfer rates and AMR. Reciprocally, plasmids with increased conjugation rates also evolved when selecting for high levels of AMR, despite the absence of susceptible hosts. Such correlated selection between plasmid transfer and AMR could increase the spread of AMR within populations and communities.