As our submission to the CRAFT shared task 2019, we present two neural approaches to concept recognition. We propose two different systems for joint named entity recognition (NER) and normalization (NEN), both of which model the task as a sequence labeling problem. Our first system is a BiLSTM network with two separate outputs for NER and NEN trained from scratch, whereas the second system is an instance of BioBERT fine-tuned on the concept-recognition task. We exploit two strategies for extending concept coverage, ontology pretraining and backoff with a dictionary lookup. Our results show that the backoff strategy effectively tackles the problem of unseen concepts, addressing a major limitation of the chosen design. In the cross-system comparison, BioBERT proves to be a strong basis for creating a concept-recognition system, although some entity types are predicted more accurately by the BiLSTM-based system.