Construction Grammar (CxG) is a paradigm from cognitive linguistics emphasising the connection between syntax and semantics. Rather than rules that operate on lexical items, it posits constructions as the central building blocks of language, i.e., linguistic units of different granularity that combine syntax and semantics. As a first step towards assessing the compatibility of CxG with the syntactic and semantic knowledge demonstrated by state-of-the-art pretrained language models (PLMs), we present an investigation of their capability to classify and understand one of the most commonly studied constructions, the English comparative correlative (CC). We conduct experiments examining the classification accuracy of a syntactic probe on the one hand and the models' behaviour in a semantic application task on the other, with BERT, RoBERTa, and DeBERTa as the example PLMs. Our results show that all three investigated PLMs are able to recognise the structure of the CC but fail to use its meaning. While human-like performance of PLMs on many NLP tasks has been alleged, this indicates that PLMs still suffer from substantial shortcomings in central domains of linguistic knowledge.