Petri net research often builds on the definition of formal properties and corresponding analysis methods. A larger share of Petri net papers provides such formal contributions, but there are also works that offer empirical insights. Such empirical insights can be highly effective in stimulating major breakthroughs even in more formal areas of computer science, such as graph algorithms or automatic image recognition. In this paper, we discuss the benefits and challenges of complementing formal research on Petri nets with an empirical research agenda. To that end, we build on a methodological framework for algorithm engineering and present selected examples of empirical works on Petri nets. These examples illustrate the spectrum of potential contributions and emphasize the salience of validity concerns. These works can serve as pillars for advancing empirical research on Petri nets.