This paper investigates the efficacy of prompt engineering techniques in enhancing both the accuracy and confidence elicitation of Large Language Models (LLMs) when applied to high-stakes medical contexts. A stratified dataset of Persian board certification exam questions, spanning multiple specialties, was used to systematically evaluate five LLMs— GPT-4o, o3-mini, Llama-3.3-70b, Llama-3.1-8b, and DeepSeek-v3. Each model underwent 156 unique configurations reflecting different temperature settings (0.3, 0.7, 1.0), prompt designs (e.g., Chain-of-Thought, Few-Shot, Emotional, Expert Mimicry), and confidence output scales (1–10, 1–100). The study employed metrics such as AUC-ROC, Brier Score, and Expected Calibration Error (ECE) to assess how accurately verbalized confidence matched real-world performance. Results revealed that while advanced prompting strategies—particularly Chain-of-Thought—consistently boosted accuracy, they also heightened overconfidence, indicating the need for post-hoc calibration. Emotional prompting inflated confidence further, potentially undermining clinical decision-making. Smaller models like Llama-3.1-8b exhibited marked underperformance across all metrics, emphasizing the importance of robust architectures in complex clinical scenarios. In contrast, proprietary models (e.g., GPT-based systems) demonstrated higher accuracy but still lacked reliable confidence calibration. These findings underscore the significance of designing prompts that effectively manage epistemic and aleatoric uncertainties, rather than solely focusing on accuracy gains. Ultimately, prompt engineering emerges as a dual-faceted approach—one that can substantially elevate model correctness yet inadvertently inflate confidence in erroneous outputs. Addressing this tension necessitates a combination of carefully crafted prompts and rigorous calibration protocols, especially where erroneous recommendations may have life-threatening consequences.