With the rise of machines to human-level performance in complex recognition tasks, a growing amount of work is directed toward comparing information processing in humans and machines. These studies are an exciting chance to learn about one system by studying the other. Here, we propose ideas on how to design, conduct, and interpret experiments such that they adequately support the investigation of mechanisms when comparing human and machine perception. We demonstrate and apply these ideas through three case studies. The first case study shows how human bias can affect the interpretation of results and that several analytic tools can help to overcome this human reference point. In the second case study, we highlight the difference between necessary and sufficient mechanisms in visual reasoning tasks. Thereby, we show that contrary to previous suggestions, feedback mechanisms might not be necessary for the tasks in question. The third case study highlights the importance of aligning experimental conditions. We find that a previously observed difference in object recognition does not hold when adapting the experiment to make conditions more equitable between humans and machines. In presenting a checklist for comparative studies of visual reasoning in humans and machines, we hope to highlight how to overcome potential pitfalls in design and inference.