Meta-learning has recently been proposed to learn models and algorithms that can generalize from a handful of examples. However, applications to structured prediction and textual tasks pose challenges for meta-learning algorithms. In this paper, we apply two meta-learning algorithms, Prototypical Networks and Reptile, to few-shot Named Entity Recognition (NER), including a method for incorporating language model pre-training and Conditional Random Fields (CRF). We propose a task generation scheme for converting classical NER datasets into the few-shot setting, for both training and evaluation. Using three public datasets, we show these meta-learning algorithms outperform a reasonable fine-tuned BERT baseline. In addition, we propose a novel combination of Prototypical Networks and Reptile.