To support a strategy to eliminate cervical cancer as a public health problem, the World Health Organisation (WHO) reviewed its guidelines for screening and treatment of cervical pre-cancerous lesions in 2021. Women living with HIV have 6-times the risk of cervical cancer compared to women in the general population, and we harnessed a model platform ('Policy1-Cervix-HIV') to evaluate the benefits and harms of a range of screening strategies for women living with HIV in Tanzania, a country with endemic HIV. Assuming 70% coverage, we found that 3-yearly primary HPV screening without triage would reduce age-standardised cervical cancer mortality rates by 72%, with a number needed to treat (NNT) of 38.7, to prevent a cervical cancer death. Triaging HPV positive women before treatment resulted in minimal loss of effectiveness and had more favorable NNTs (19.7-33.0). Screening using visual inspection with acetic acid (VIA) or cytology was less effective than primary HPV and, in the case of VIA, generated a far higher NNT of 107.5. These findings support the WHO 2021 recommendation that women living with HIV are screened with primary HPV testing in a screen-triage-and-treat approach starting at 25 years, with regular screening every 3-5 years.