Background: Pragmatic language impairment in children with specific language impairment has proved difficult to assess, and the nature of their abilities to comprehend pragmatic meaning has not been fully investigated. Aims: To develop both a cognitive approach to pragmatic language assessment based on Relevance Theory and an assessment tool for identifying a group of children with pragmatic language impairment from within an specific language impairment group. Methods & Procedures: The authors focused on Relevance Theory's view of the role of context in pragmatic language comprehension using questions of increasing pragmatic complexity in different verbal contexts (scenarios with and without pictures and a story with supporting pictures). The performances of the children with and without pragmatic impairment on the most pragmatically demanding Implicature questions were examined. This study included 99 children: 27 with specific language impairment (including nine pragmatically impaired children) and two groups of typically developing children (32 children aged 5-6 years and 40 children aged 7-11 years). Outcomes & Results: The specific language impairment group performed similarly to their peers when utilizing context in inferring referents, inferring semantic meaning, and generating Implicatures, only when the answer was provided by pictorial context. Both the children with specific language impairment and the 5-6 year olds were not yet competent at utilizing verbal context when answering the most pragmatically demanding questions (targeting Implicature). On these questions the children with pragmatic language impairment performed significantly poorer than the rest of the specific language impairment group and performance scores on Implicature questions were found to identify accurately the children with pragmatic language impairment from the rest of the specific language impairment group (sensitivity = 89%). Conclusions: Children's ability to infer and integrate information in the comprehension of pragmatic meaning was found to be influenced by the available context. As children become more competent they are able to utilize verbal context and integrate information. Children with specific language impairment and those with pragmatic language impairment were found to be developmentally delayed at making inferences, but children with pragmatic language impairment had particular difficulty in integrating contextual information. Findings support the view that a cognitive approach to assessing pragmatic comprehension deficits could provide clinicians with a useful tool. (Contains 6 tables, 2 figures and 1 note.)