Building computational models of engineered exemplars, or prototypes, is a common practice in the bioengineering sciences. Computational models in this domain are often built in a patchwork fashion, drawing on data and bits of theory from many different domains, and in tandem with actual physical models, as the key objective is to engineer these prototypes of natural phenomena. Interestingly, such patchy model building, often combined with visualizations, whose format is open to a wide range of choice, leads to the discovery of new concepts and control structures. Two key questions are raised by this practice: how could discoveries arise from building external representations for which there is wide latitude in choice of the components from which they are built, and thus can be considered significantly arbitrary, and how could such discoveries allow engineering a real-world prototype system. To examine these questions, we present two case studies of discoveries that emerged from the building of such computational models in the bioengineering sciences. We then develop a process model that accounts for the discovery and transfer problems raised by both these cases, focusing on the process of building the model. Specifically, to account for the discovery problem, we propose that the process of building such models gradually leads to a close coupling between the modeler’s internal processes and the external dynamic model. To account for the transfer problem, we propose that the process of building the model leads to the creation of an enactive model that is generic, which closely enacts, and thus reveals, the way the system-level behavior of the engineered prototype emerges in time through the interaction of its parts. This enactive replication process leads to the model and the prototype forming a new class, which allows concepts and control structures developed for the computational model to be transfered to the real-world prototype. We argue that this account requires rethinking correspondence in engineering sciences as a plastic and enactive relation. A closer focus on the process of building models is required to develop a general account of this emerging approach to discovery.