RNA-protein binding is critical to gene regulation, controlling fundamental processes including splicing, translation, localization and stability, and aberrant RNA-protein interactions are known to play a role in a wide variety of diseases. However, molecular understanding of RNA-protein interactions remains limited, and in particular identification of the RNA motifs that bind proteins has long been a difficult problem. To address this challenge, we have developed a novel semi-automatic algorithm, SARNAclust, to computationally identify combined structure/sequence motifs from immunoprecipitation data. SARNAclust is, to our knowledge, the first unsupervised method that can identify RNA motifs at full structural resolution while also being able to simultaneously deconvolve multiple motifs. SARNAclust makes use of a graph kernel to evaluate similarity between sequence/structure objects, and provides the ability to isolate the impact of specific features through a bulge graph formalism. SARNAclust also includes a key method for predicting RNA secondary structure at CLIP peaks, RNApeakFold, that we have verified to be effective on synthetic motif data. We applied SARNAclust to 30 ENCODE eCLIP datasets, identifying known motifs and novel predictions. Notably, we predicted a new motif for the protein ILF3 similar to that for the splicing factor hnRNPC, providing evidence for interaction between these proteins. To validate our predictions and test specific features that impact binding, we performed a directed RNA bind-n-seq assay for two proteins: ILF3 and SLBP, in each case revealing the combined importance of RNA sequence and structure to protein binding. Availability: https://github.com/idotu/SARNAclust