During the last decade, children have shown an increasing need for mental wellbeing interventions due to their anxiety and depression issues, which the COVID-19 pandemic has exacerbated. Socially Assistive Robotics have been shown to have a great potential to support children with mental wellbeing-related issues. However, understanding how robots can be used to aid the measurement of these issues is still an open challenge. This paper presents a narrative review of child-robot interaction (cHRI) papers (IEEE ROMAN proceedings from 2016–2021 and (...) keyword-based article search using Google Scholar) to investigate the open challenges and potential knowledge gaps in the evaluation of mental wellbeing or the assessment of factors affecting mental wellbeing in children. We exploited the SPIDER framework to search for the key elements for the inclusion of relevant studies. Findings from this work (10 screened papers in total) investigate the challenges in cHRI studies about mental wellbeing by categorising the current research in terms of robot-related factors (robot autonomy and type of robot), protocol-related factors (experiment purpose, tasks, participants and user sensing) and data related factors (analysis and findings). The main contribution of this work is to highlight the potential opportunities for cHRI researchers to carry out measurements concerning children’s mental wellbeing. (shrink)