Natural language processing systems often struggle with out-of-vocabulary (OOV) terms, which do not appear in training data. Blends, such as "innoventor", are one particularly challenging class of OOV, as they are formed by fusing together two or more bases that relate to the intended meaning in unpredictable manners and degrees. In this work, we run experiments on a novel dataset of English OOV blends to quantify the difficulty of interpreting the meanings of blends by large-scale contextual language models such as BERT. We first show that BERT's processing of these blends does not fully access the component meanings, leaving their contextual representations semantically impoverished. We find this is mostly due to the loss of characters resulting from blend formation. Then, we assess how easily different models can recognize the structure and recover the origin of blends, and find that context-aware embedding systems outperform character-level and context-free embeddings, although their results are still far from satisfactory.