Estimation of a model's confidence on its outputs is critical for Conversational AI systems based on large language models (LLMs), especially for reducing hallucination and preventing over-reliance. In this work, we provide an exhaustive exploration of methods, including approaches proposed for open- and closed-weight LLMs, aimed at quantifying and leveraging model uncertainty to improve the reliability of LLM-generated responses, specifically focusing on dialogue state tracking (DST) in task-oriented dialogue systems (TODS). Regardless of the model type, well-calibrated confidence scores are essential to handle uncertainties, thereby improving model performance. We evaluate four methods for estimating confidence scores based on softmax, raw token scores, verbalized confidences, and a combination of these methods, using the area under the curve (AUC) metric to assess calibration, with higher AUC indicating better calibration. We also enhance these with a self-probing mechanism, proposed for closed models. Furthermore, we assess these methods using an open-weight model fine-tuned for the task of DST, achieving superior joint goal accuracy (JGA). Our findings also suggest that fine-tuning open-weight LLMs can result in enhanced AUC performance, indicating better confidence score calibration.