There has been longstanding interest in students' aesthetic feelings in engaging with school science, but new multimodal accounts of meaning-making, and changing curricular goals where science is integrated with other subjects, pose new methodological challenges for researching these feelings. In this paper, we aim to synthesise relevant literature as the bases for proposing methodological practices to address these new research challenges. We draw on past and current pragmatist and semiotic perspectives to justify our methodological approach. We claim that research on aesthetic feelings needs to identify: (a) the complex nature of aesthetic meaning/feeling processes and multiple influences on these processes and (b) short-term and longer-term consequences on participants' taste for, and learning in, science. Building on a practical epistemology, we propose that these questions can be addressed through multimodal analyses of aesthetic intentions and responses when embedded in teacher and student inquiry purposes, discursive interactions, artefact-making, and evaluative feelings/judgements. To illustrate the scope and challenges of these methodological strategies, we draw on examples of analyses in companion papers in this special issue, both when science is taught alone and when integrated with other subjects.