Large language models (LLMs) exhibit advanced reasoning skills, enabling robots to comprehend natural language instructions and strategically plan high-level actions through proper grounding. However, LLM hallucination may result in robots confidently executing plans that are misaligned with user goals or, in extreme cases, unsafe. Additionally, inherent ambiguity in natural language instructions can induce task uncertainty, particularly in situations where multiple valid options exist. To address this issue, LLMs must identify such uncertainty and proactively seek clarification. This paper explores the concept of introspective planning as a systematic method for guiding LLMs in forming uncertainty--aware plans for robotic task execution without the need for fine-tuning. We investigate uncertainty quantification in task-level robot planning and demonstrate that introspection significantly improves both success rates and safety compared to state-of-the-art LLM-based planning approaches. Furthermore, we assess the effectiveness of introspective planning in conjunction with conformal prediction, revealing that this combination yields tighter confidence bounds, thereby maintaining statistical success guarantees with fewer superfluous user clarification queries.