Socially Assistive Robots (SARs) show promise in helping children during therapeutic and clinical interventions. However, using SARs for the evaluation of mental wellbeing of children has not yet been explored. Thus, this paper presents an empirical study with 28 children 8-13 years old interacting with a Nao robot in a 45-minute session where the robot administered (robotised) the Short Mood and Feelings Questionnaire (SMFQ) and the Revised Child Anxiety and Depression Scale (RCADS). Prior to the experimental session, we also evaluated children’s wellbeing using established standardised approaches via online RCADS questionnaires filled by the children (self-report) and their parents (parent-report). We clustered the participants into three groups (lower, medium, and higher tertile) based on their SMFQ scores. Further, we analysed the questionnaire response across the three clusters and across the different modes of administration (self-report, parent-report, and robotised). Our results show that the robotised evaluation seems to be the most suitable mode in identifying wellbeing related anomalies in children across the three clusters of participants as compared with the self-report and the parent-report modes. Further, children with decreasing levels of wellbeing (lower, medium and higher tertiles) exhibit different response patterns: children of higher tertile are more negative in their responses to the robot while the ones of lower tertile are more positive in their responses to the robot. Findings from this work show that SARs can be a promising tool to potentially evaluate mental wellbeing related concerns in children.