This chapter delves into the implications of generative AI hallucinations, particularly focusing on how they challenge the principles of prompt engineering and creative applications within the healthcare field. These hallucinations occur when AI systems generate information that appears plausible but is factually incorrect or unsupported by data. In healthcare, where accuracy and reliability are paramount, AI hallucinations can have severe consequences. Prompt engineering, the practice of designing effective prompts for AI models, plays a crucial role in mitigating the risks caused by AI hallucinations. The chapter surveys the best practices of prompt engineering in the context of healthcare (precision and clarity; ethical considerations and bias mitigation; iterative refinement and user feedback; incorporating multimodal inputs; human oversight), exploring its key principles and strategies to minimise AI hallucinations (incorporating constraints and boundaries; incorporating structured formats; providing contextual specificity; keeping a balance between innovation and reliability). Afterwards, the chapter explores a controversial relationship between AI hallucinations and creativity. It shows that AI hallucinations have been primarily associated with negative consequences. However, their potentially positive role deserves exploration in several healthcare areas, such as drug design, innovative treatment approaches, creative thinking stimulation, medical training and education, and patient engagement.