Computational methods, in particular text-as-data or Natural Language Processing (NLP) approaches, have become popular to study climate change communication as a global and large-scale phenomenon. Scholars have discussed opportunities and challenges of these methods for climate change communication, with some proponents and critics taking strong positions, either embracing the potential of computational methods or critically questioning their value. Mirroring developments in the broader social scientific debate, we aim to bring both sides together by proposing a reflexive, integrative approach for computational research on climate change communication: We reflect on strengths (e.g., making data big and small, nowcasting observations) and weaknesses (e.g., introducing empiricist epistemologies, ignoring biases) of computational approaches. Moreover, we also provide concrete and constructive guidance on when and how to integrate (or not integrate) these methods based on theoretical considerations. We thereby understand computational methods as part of an ever-increasing, diverse toolbox for analyzing climate change communication.