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Different retrofitting measures can be implemented at different levels of the industrial furnace, such as refractory layers, energy recovery solutions, new burners and fuel types, and monitoring and control systems. However, there is a high level of uncertainty about the possible implications of integrating new technologies, not only in the furnace but also on the upstream and downstream processes. In this regard, there is a lack of holistic approaches to design the optimal system configurations under a multicriteria perspective, especially when innovative technologies and multi-sectorial processes are involved. The present work proposes a holistic approach to natural gas melting and heating furnaces in energy-intensive industries. A multicriteria analysis, based on criteria and subcriteria, is applied to select the most profitable retrofitting solution using the analytic hierarchy process and stakeholder expertise. The methodology is based on technical indicators, i.e., life cycle assessment, life cycle cost, and thermoeconomic analysis, for evaluating the current state of existing natural gas furnaces. Once the current state is characterized, the methodology determines the potential of efficiency improvement, environmental impact reduction, and cost-savings caused mainly by the implementation of new retrofitting solutions including new refractories, new burner concepts (co-firing), and innovative energy recovery solutions based on phase change materials. Therefore, this methodology can be considered as the first stage that guarantees technical, environmental, and economic feasibility in evaluating the effects of new technologies on the overall system performance.