Conventional implicatures are omnipresent in daily life communication but experimental research on this topic is sparse, especially research with children. The aim of this study was to investigate if eight- to twelve-year-old children spontaneously make the conventional implicature induced by but, so, and nevertheless in ‘p but q’ sentences. Additionally, the study aimed to shed light on the cognitive effort required for these inferences by measuring working memory (WM) capacity. Our results show that children do make these inferences to a certain extent, but are sensitive to the content of the arguments. We found a significant effect of sentence type, but did not observe any developmental effect, nor any effect of WM: a higher age or WM capacity does not result in more pragmatic inferences.