Large language models are increasingly deployed in clinical settings, but their reliability remains uncertain—they hallucinate facts, behave inconsistently across instruction phrasings, and struggle with evolving medical terminology. In my talk, I address methods to systematically evaluate clinical LLM reliability across four dimensions aligned with how healthcare professionals actually work: verifying concrete facts (FactEHR), ensuring stable guidance across instruction variations (instruction sensitivity studies show a large variation in model performances), assessing LLMs on real patient conversations. These contributions establish evaluation standards spanning factuality, robustness and patient-centered communication, charting a path toward clinical AI that is safer, more equitable, and more trustworthy.