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The momentum of the Fourth Industrial Revolution is driving increased demand for certain specific metals. These include copper, silver, gold, and platinum group metals (PGMs), which have important applications in renewable energies, green hydrogen, and electronic products. However, the continuous extraction of these metals is leading to a rapid decline in their ore grades and, consequently, increasing the environmental impact of extraction. Hence, obtaining metals from secondary sources, such as waste electrical and electronic equipment (WEEE), has become imperative for both environmental sustainability and ensuring their availability. To evaluate the sustainability of the process, this paper proposes using an exergy approach, which enables appropriate allocation among co-products, as well as the assessment of exergy losses and the use of non-renewable resources. As a case study, this paper analyzes the recycling process of waste printed circuit boards (PCBs) by disaggregating the exergy cost into renewable and non-renewable sources, employing different exergy-based cost allocation methods for the mentioned metals. It further considers the complete life cycle of metals using the Circular Thermoeconomics methodology. The results show that, when considering the entire life cycle, between 47% and 53% of the non-renewable exergy is destroyed during recycling. Therefore, delaying recycling as much as possible would be the most desirable option for minimizing the use of non-renewable resources. [ABSTRACT FROM AUTHOR]