<p>This study investigates how green food certification influences customer engagement behaviour through the mediating roles of perceived value and perceived authenticity. Using online survey data collected from 302 food consumers in Shandong Province, China, in 2023, this research employs structural equation modelling within a stimulus–organism–response (S-O-R) framework to examine the proposed relationships. The results show that green food certification has a significant positive direct effect on customer engagement behaviour and indirect effects through both perceived value and perceived authenticity, which act as parallel mediators. Further analysis reveals that certification authority strengthens the effect of certification on perceived value, while price tolerance positively moderates the relationship between perceived value and customer engagement behaviour. However, customer demographic characteristics do not exhibit significant moderating effects. These findings extend the literature on green certification by linking it to nontransactional customer engagement and by clarifying the psychological mechanisms underlying consumer responses to certified green food. The study provides practical insights for policymakers and food enterprises seeking to promote sustainable consumption and enhance the effectiveness of green certification systems.</p>