The most meaningful connections between people are often fostered through expression of shared vulnerability and emotional experiences in personal narratives. We introduce a new task of identifying similarity in personal stories based on empathic resonance, i.e., the extent to which two people empathize with each others’ experiences, as opposed to raw semantic or lexical similarity, as has predominantly been studied in NLP. Using insights from social psychology, we craft a framework that operationalizes empathic similarity in terms of three key features of stories: main events, emotional trajectories, and overall morals or takeaways. We create EmpathicStories, a dataset of 1,500 personal stories annotated with our empathic similarity features, and 2,000 pairs of stories annotated with empathic similarity scores. Using our dataset, we fine-tune a model to compute empathic similarity of story pairs, and show that this outperforms semantic similarity models on automated correlation and retrieval metrics. Through a user study with 150 participants, we also assess the effect our model has on retrieving stories that users empathize with, compared to naive semantic similarity-based retrieval, and find that participants empathized significantly more with stories retrieved by our model. Our work has strong implications for the use of empathy-aware models to foster human connection and empathy between people.