Artificial Intelligence (AI) presents significant opportunities for new business ventures within the industrial domain. However, its adoption introduces a broad spectrum of risk sources across dimensions such as cybersecurity, reliability, robustness, safety, transparency, or human oversight. Simultaneously, organizations are confronted with an increasing amount of digital and AI-based legislation in the international environment. This leads to a fragmented landscape of legal and risk-related requirements, often inconsistent, overlapping, and duplicated. This results in high uncertainty and bureaucratic burden during the development and deployment of AI products. To address these challenges, a systematic, responsible, and efficient approach is required to handle the complex legal requirements as well as the emerging wide range of risk sources. Responsible AI Engineering describes such a systematic approach, enabling the efficient and innovative development of AI products while ensuring compliance with the complex and fragmented legal landscape. In this paper, we introduce the Generative AI Risk Management (GARM) methodology as an instantiation of Responsible AI Engineering. We demonstrate through a concrete industrial GenAI-based product how the GARM methodology enables organizations to drive AI innovation compliantly and with heightened risk awareness.