Federated Learning (FL) methods adopt efficient communication technologies to distribute machine learning tasks across edge devices, reducing the overhead in terms of data storage and computational complexity compared to centralized solutions. Rather than moving large data volumes from producers (sensors, machines) to energy-hungry data centers, raising environmental concerns due to resource demands, FL provides an alternative solution to mitigate the energy demands of several learning tasks while enabling new Artificial Intelligence of Things (AIoT) applications. This paper proposes a framework for real-time monitoring of the energy and carbon footprint impacts of FL systems. The carbon tracking tool is evaluated for consensus (fully decentralized) and classical FL policies. For the first time, we present a quantitative evaluation of different computationally and communication efficient FL methods from the perspectives of energy consumption and carbon equivalent emissions, suggesting also general guidelines for energy-efficient design. Results indicate that consensus-driven FL implementations should be preferred for limiting carbon emissions when the energy efficiency of the communication is low (i.e., < 25 Kbit/Joule). Besides, quantization and sparsification operations are shown to strike a balance between learning performances and energy consumption, leading to sustainable FL designs.