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 increasingly used preregistration-have been designed for purely experimental work that tests straightforward hypotheses with standard inferential statistical analyses, such as assessing whether an experimental manipulation has an effect on a variable of interest. But psychology is a diverse field of research. 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 intricate 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 Crüwell et al. (Crüwell S, Stefan AM, Evans NJ. 2019 Robust standards in cognitive science. Comput. Brain Behav. 2, 255-265) labelled model application, where researchers apply a cognitive model as a measurement tool to test hypotheses about parameters of the cognitive model. Specifically, we (i) discuss several potential researcher degrees of freedom within model application, (ii) provide the first preregistration template for model application and (iii) provide an example of a preregistered model application using our preregistration template. More broadly, we hope that our discussions and concrete proposals constructively advance the mostly abstract current debate surrounding preregistration in cognitive modelling, and provide a guide for how preregistration templates may be developed in other diverse or intricate research contexts.