Empowering large language models (LLMs) to accurately express confidence in their answers is essential for reliable and trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks—confidence calibration and failure prediction—across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve, yet still far from ideal performance. 3) Human-inspired prompting strategies mitigate this overconfidence, albeit with diminishing returns in advanced models like GPT-4, especially in improving failure prediction. 4) Employing sampling strategies paired with specific aggregators can effectively enhance failure prediction; moreover, the choice of aggregator can be tailored based on the desired performance enhancement. Despite these advancements, all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.