To facilitate robust and trustworthy deployment of large language models (LLMs), it is essential to quantify the reliability of their generations through uncertainty estimation. While recent efforts have made significant advancements by leveraging the internal logic and linguistic features of LLMs to estimate uncertainty scores, our empirical analysis highlights the pitfalls of these methods to strike a harmonized estimation between indication, balance, and calibration, which hinders their broader capability for accurate uncertainty estimation. To address this challenge, we propose CUE (Corrector for Uncertainty Estimation): A straightforward yet effective method that employs a lightweight model trained on data aligned with the target LLM's performance to adjust uncertainty scores. Comprehensive experiments across diverse models and tasks demonstrate its effectiveness, which achieves consistent improvements of up to 60% over existing methods.