In recent years, open science practices have become increasingly popular in psychology and related sciences. These practices aim to increase rigour and transparency in science as a potential response to the challenges posed by the replication crisis. Many of these reforms – including the highly influential preregistration – have been designed for experimental work that tests simple hypotheses with standard statistical analyses, such as assessing whether an experimental manipulation has an effect on a variable of interest. However, psychology is a diverse field of research, and the somewhat narrow focus of the prevalent discussions surrounding and templates for preregistration has led to debates on how appropriate these reforms are for areas of research with more diverse hypotheses and more complex methods of analysis, such as cognitive modelling research within mathematical psychology. Our article attempts to bridge the gap between open science and mathematical psychology, focusing on the type of cognitive modelling that Cruwell, Stefan, and Evans (2019) labelled model application, where researchers apply a cognitive model as a measurement tool to test hypotheses about parameters of the cognitive model. Specifically, we 1) discuss several potential researcher degrees of freedom within model application, 2) provide the first preregistration template for model application, and 3) provide an example of a preregistered model application using our preregistration template. More broadly, we hope that our discussions and proposals constructively advance the debate surrounding preregistration in cognitive modelling, and provide a guide for how preregistration templates may be developed in other diverse or complex research contexts."