As large language models are increasingly used for contract drafting, case research and even judicial work, a central question is how to make their outputs trustworthy. This survey addresses that question through the lens of verified generation for legal AI, focusing on systems that are robust against hallucinations and traceable to authoritative legal sources. First, we propose a unified framework for verified generation in legal AI, linking reasoning, retrieval, and validation around factual reliability. Second, we cast reliability methods into two paradigms of epistemic negotiation, by failure and by conflict, enabling models to recognize and act on their competence limits. Third, we survey the legal-AI landscape and identify challenges for verifiable, governance-native systems. This survey outlines a roadmap for trustworthy legal AI and for reliable reasoning beyond the legal domain.