Maritime transport is one of the most energy efficient and one of the lowest CO2 emitting modes of transport. Nonetheless, the industry's carbon footprint is significant. Stakeholders recognize the need for continuing efforts to curb CO2 emissions. Such efforts require the ability to measure individual vessels' energy efficiency. To this end, several energy efficiency metrics/indices have been developed for tracking real time CO2 emissions by marine vessels. We propose a new methodology to calculate and monitor individual vessel's energy efficiency and carbon emissions in real time through the Real-Time Energy Efficiency Operating Index (RT-EEOI).We demonstrate the practicality of the proposed methodology by presenting a software architecture implementing it. Specifically, by combining a vessel database with live data from the Automated Identification System (AIS), we calculate the RTEEOI index. The system has been deployed to monitor traffic in the Southwest part of the port and strait of Singapore. We propose an example of implementation of the proposed framework in the Singapore waters to show how it can be deployed in the scenario of real time efficiency tracking.