Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, yet they generally lack self-awareness—often displaying overconfidence when confronted with questions beyond their knowledge boundaries. This limitation severely hinders their trustworthiness in high-stakes scenarios. Existing calibration methods typically rely on sampling accuracy—derived from multiple outputs—as a proxy for model confidence. However, this coarse-grained metric fails to capture the model’s internal cognitive states, such as confusion, hallucination, or persistent belief in false knowledge. To address this, we propose \texttt{CogConf} (Cognitive Confidence), a cognitively grounded uncertainty signal that extends sampling accuracy by incorporating the semantic diversity of incorrect answers and the model’s abstention behaviors. By shifting the focus from sampling-based to cognition-oriented uncertainty modeling, \texttt{CogConf} offers a more faithful reflection of the model's internal beliefs. Building on this signal, we introduce \textsc{CogAlign}, a simple yet effective alignment framework that explicitly aligns the model’s verbalized confidence with \texttt{CogConf}, thereby producing uncertainty estimates that better reflect the model’s internal cognition. Experimental results on six knowledge-intensive in-domain and out-of-domain QA datasets demonstrate that \texttt{CogConf} robustly characterizes the model's internal uncertainty. Building on this foundation, \textsc{CogAlign} guides the model's expression to significantly enhance the trustworthiness and utility of its uncertainty calibration without compromising its underlying QA capabilities, while also demonstrating strong cross-task generalization and output stability. Offering a new pathway toward building more trustworthy LLMs.