Large language models (LLMs) have offered new opportunities for emotional support, and recent work has shown that they can produce empathic responses to people in distress. However, long-term mental well-being requires emotional self-regulation, where a one-time empathic response falls short. This work takes a first step by engaging with cognitive reappraisals, a strategy from psychology practitioners that uses language to targetedly change negative appraisals that an individual makes of the situation; such appraisals is known to sit at the root of human emotional experience. We hypothesize that psychologically grounded principles could enable such advanced psychology capabilities in LLMs, and design RESORT which consists of a series of reappraisal constitutions across multiple dimensions that can be used as LLM instructions. We conduct a first-of-its-kind expert evaluation (by clinical psychologists with M.S. or Ph.D. degrees) of an LLM's zero-shot ability to generate cognitive reappraisal responses to medium-length social media messages asking for support. This fine-grained evaluation showed that even LLMs at the 7B scale guided by RESORT are capable of generating empathic responses that can help users reappraise their situations.