The treatment of infections caused by antibiotic-resistant bacteria is one of the great challenges faced by clinicians in the 21st century. Antibiotic resistance genes are often transferred between bacteria by mobile genetic vectors called plasmids. It is commonly believed that removal of antibiotic pressure will reduce the numbers of antibiotic-resistant bacteria due to the perception that carriage of resistance imposes a fitness cost on the bacterium. This study investigated the ability of the plasmid pCT, a globally distributed plasmid that carries an extended-spectrum-β-lactamase (ESBL) resistance gene (bla(CTX-M-14)), to persist and disseminate in the absence of antibiotic pressure. We investigated key attributes in plasmid success, including conjugation frequencies, bacterial-host growth rates, ability to cause infection, and impact on the fitness of host strains. We also determined the contribution of the bla(CTX-M-14) gene itself to the biology of the plasmid and host bacterium. Carriage of pCT was found to impose no detectable fitness cost on various bacterial hosts. An absence of antibiotic pressure and inactivation of the antibiotic resistance gene also had no effect on plasmid persistence, conjugation frequency, or bacterial-host biology. In conclusion, plasmids such as pCT have evolved to impose little impact on host strains. Therefore, the persistence of antibiotic resistance genes and their vectors is to be expected in the absence of antibiotic selective pressure regardless of antibiotic stewardship. Other means to reduce plasmid stability are needed to prevent the persistence of these vectors and the antibiotic resistance genes they carry.