Background In cluster-randomized controlled trials (C-RCTs) of HIV prevention strategies, HIV incidence is expensive to measure directly. Surveillance data on HIV diagnoses or viral suppression could provide cheaper incidence estimates. We used mathematical modelling to evaluate whether these measures can replace HIV incidence measurement in C-RCTs. Methods We used a US HIV transmission model to simulate C-RCTs of expanded antiretroviral therapy(ART), pre-exposure prophylaxis(PrEP) and HIV testing, together or alone. We tested whether modelled reductions in total new HIV diagnoses, diagnoses with acute infection, diagnoses with early infection(CD4 > 500 cells/μl), diagnoses adjusted for testing volume, or the proportion virally non-suppressed, reflected HIV incidence reductions. Results Over a two-year trial expanding PrEP alone, modelled reductions in total diagnoses underestimated incidence reductions by a median six percentage points(pp), with acceptable variability(95 % credible interval -14,-2pp). For trials expanding HIV testing alone or alongside ART + PrEP, greater, highly variable bias was seen[-20pp(-128,-1) and -30pp(-134,-16), respectively]. Acceptable levels of bias were only seen over longer trial durations when levels of awareness of HIV-positive status were already high. Expanding ART alone, only acute and early diagnoses reductions reflected incidence reduction well, with some bias[-3pp(-6,-1) and -8pp(-16,-3), respectively]. Early and adjusted diagnoses also reliably reflected incidence when scaling up PrEP alone[bias -5pp(-11,1) and 10pp(3,18), respectively]. For trials expanding testing (alone or with ART + PrEP), bias for all measures explored was too variable for them to replace direct incidence measures, unless using diagnoses when HIV status awareness was already high. Conclusions Surveillance measures based on HIV diagnoses may sometimes be adequate surrogates for HIV incidence reduction in C-RCTs expanding ART or PrEP only, if adjusted for bias. However, all surveillance measures explored failed to approximate HIV incidence reductions for C-RCTs expanding HIV testing, unless levels of awareness of HIV-positive status were already high.