Vaccine hesitancy is one of the main threats to global health, as became clear once more during the COVID-19 pandemic. Vaccination campaigns could benefit from appeals to social norms to promote vaccination, but without awareness of the social norm in place any intervention relying on social norms may backfire. We present a two-step approach of social norm diagnosis and intervention that identifies both whether a vaccination norm exists or develops over time and corrects misperceptions. In two studies ( and ) conducted in Rome, Italy from June to August 2021 (during the first COVID-19 vaccination campaign), we show that vaccine-hesitant people strongly underestimated vaccine acceptance rates for COVID-19 despite increases in region-wide vaccination rates. This suggests a false consensus bias on the social norm of vaccination. We presented a subgroup of vaccine-hesitant people with the accurate vaccine acceptance rates (both planned uptake and vaccine approval) and tested if this social information would lower their vaccine hesitancy. We do not find clear effects, most likely because of the introduction of the COVID-19 health certificate (the "green pass") that was implemented during our data collection. The green pass reduced both misperceptions in the social norm and vaccine hesitancy, thus undermining our treatment effect. We conclude that to alleviate misperceptions on the social norm of vaccination in early stages of the vaccination campaign governments and media should report not just the current vaccination rate, but also about vaccination intentions and approval.