Emergent language is unique among fields within the discipline of machine learning for its open-endedness, not obviously presenting well-defined problems to be solved. As a result, the current research in the field has largely been exploratory: focusing on establishing new problems, techniques, and phenomena. Yet after these problems have been established, subsequent progress requires research which can measurably demonstrate how it improves on prior approaches. This type of research is what we call systematic research; in this paper, we illustrate this mode of research specifically for emergent language. We first identify the overarching goals of emergent language research, categorizing them as either science or engineering. Using this distinction, we present core methodological elements of science and engineering, analyze their role in current emergent language research, and recommend how to apply these elements.