Plasmids may maintain antibiotic resistance genes in bacterial populations through conjugation, in the absence of direct selection pressure. However, the costs and benefits of conjugation for plasmid and bacterial fitness are not well understood. Using invasion and competition experiments with plasmid mutants we explicitly tested how conjugation contributes to the maintenance of a plasmid bearing a single extended-spectrum ß-lactamase (ESBL) gene (blaCTX-M-14). Surprisingly, conjugation had little impact on overall frequencies, although it imposed a substantial fitness cost. Instead, stability resulted from the plasmid conferring fitness benefits when rare. Frequency dependent fitness did not require a functional blaCTX-M-14 gene, and was independent of culture media. Fitness benefits when rare are associated with the core plasmid backbone but are able to drive up frequencies of antibiotic resistance because fitness burden of the blaCTX-M-14 gene is very low. Negative frequency dependent fitness can contribute to maintaining a stable frequency of resistance genes in the absence of selection pressure from antimicrobials. In addition, persistent, low cost resistance has broad implications for antimicrobial stewardship.