Assessing how well a large language model (LLM) understands human, rather than merely text, remains an open challenge. To bridge the gap, we introduce Sentient Agent as a Judge (SAGE), an automated evaluation framework that measures an LLM's higher-order social cognition. SAGE instantiates a Sentient Agent that simulates human-like emotional changes and inner thoughts during interaction, providing a more realistic evaluation of the tested model in multi-turn conversations. At every turn, the agent reasons about (i) how its emotion changes, (ii) how it feels, and (iii) how it should reply, yielding a numerical emotion trajectory and interpretable inner thoughts. Experiments on 100 supportive-dialogue scenarios show that the final Sentient emotion score correlates strongly with Barrett-Lennard Relationship Inventory (BLRI) ratings and utterance-level empathy metrics, validating psychological fidelity. We also build a public Sentient Leaderboard covering 18 commercial and open-source models that uncovers substantial gaps (up to 4x) between frontier systems (GPT-4o-Latest, Gemini2.5-Pro) and earlier baselines, gaps not reflected in conventional leaderboards (e.g., Arena). SAGE thus provides a principled, scalable and interpretable tool for tracking progress toward genuinely empathetic and socially adept language agents.