Computational construction grammar aims to provide concrete processing models that operationalise construction grammar accounts of the different aspects of language. This paper discusses the computational mechanisms that allow construction grammar models to exhibit, to a certain extent, the creativity and inventiveness that is observed in human language use. It addresses two main types of language-related creativity. The first type concerns the 'free combination of constructions,' which gives rise to the open-endedness of language. The second type concerns the 'appropriate violation of usual constraints' that permits language users to go beyond what is possible when adhering to the usual constraints of the language, and be truly creative by relaxing these constraints and by introducing novel constructions. All mechanisms and examples discussed in this paper are fully operationalised and implemented in Fluid Construction Grammar.