There is increasing concern about Mycoplasma genitalium as a cause of urethritis, cervicitis, pelvic inflammatory disease (PID), infertility and ectopic pregnancy. Commercial nucleic acid amplification tests (NAATs) are becoming available, and their use in screening for M. genitalium has been advocated, but M. genitalium's natural history is poorly-understood, making screening's effectiveness unclear. We used a transmission-dynamic compartmental model to synthesise evidence from surveillance data and epidemiological and behavioural studies to better understand M. genitalium's natural history, and then examined the effects of implementing NAAT testing. Introducing NAAT testing initially increases diagnoses, by finding a larger proportion of infections; subsequently the diagnosis rate falls, due to reduced incidence. Testing only symptomatic patients finds relatively little infection in women, as a large proportion is asymptomatic. Testing both symptomatic and asymptomatic patients has a much larger impact and reduces cumulative PID incidence in women due to M. genitalium by 31.1% (95% range:13.0%-52.0%) over 20 years. However, there is important uncertainty in M. genitalium's natural history parameters, leading to uncertainty in the absolute reduction in PID and sequelae. Empirical work is required to improve understanding of key aspects of M. genitalium's natural history before it will be possible to determine the effectiveness of screening.