Constructing and critiquing evidence-based claims is centrally important to aspiring medical professionals and to scientists more generally. Accordingly, The National Academy of Science's "Framework for K-12 Science Education" describes engaging in argument from evidence as one of the practices that characterize work in science. However, despite the central role argumentation plays in construction and refinement of evidence-based explanations and models, it is very often absent from K-16 science learning environments. Here, we frame argumentation from spectroscopic evidence in terms of flexible application of a series of procedures to pull information from spectroscopic traces and use this evidence to inform claims as to the structure of an unknown molecule. Through analysis of responses to several multipart assessment items, we examined how students analyzed, interpreted and used spectroscopic evidence to inform their claims. We found that students were fairly adept at analyzing and interpreting data from infrared and [superscript 13]C NMR traces as well as indicating correspondence between proton environments in their structural prediction and appropriate [superscript 1]H NMR peaks. Unfortunately, none of these tasks were significantly associated with student success in proposing a claim consistent with an entire corpus of spectroscopic data. Further, scaffolding of the task prompt had no impact on student ability to successfully construct evidence-based structural predictions. Our findings indicate that students will require significant support to use their procedural knowledge flexibly in order to iteratively construct and critique claims supported by spectroscopic evidence.