The Web of Things (WoT) defines the idea of addressing and requesting any surrounding connected device through web applications. These devices are for a large part, tiny, wireless and mostly battery-powered. Therefore, energy represents a critical limiting resource for their large scale deployment in real life applications, such as smart cities or smart buildings. Consequently, the ability to measure, track and finely profile energy consumption of such devices and correlate it with the application driving the device functionalities is a big challenge to improve the development of WoT embedded applications. In this paper, we present our recent ongoing works on energy consumption measurement of networked embedded applications for the WoT area. More particularly, we focus on measuring energy consumption of the well-known Contiki Operating System HTTP web server using two measurement methods, a simulation based method and a real world software based measurement method. Doing this, we quantify and model the gap existing between the simulation and the real world regarding network embedded applications, such as embedded web servers. Afterwards, we describe our aims in using a real world hardware energy consumption measurement method and profile a home-made embedded web server prototype called Smews. This latter could theoretically improve performances and power consumption of WoT applications relying on TCP/IP protocol.