Smart metering IoT applications are among the most energy-critical in the current panorama. Metering sensors are battery-powered and are expected to have a lifetime exceeding ten years. In order to achieve such long operation duration, a generic header compression mechanism named Static Context Header Compression (SCHC) has been introduced and accepted as a standard by the Internet Engineering Task Force (IETF). This paper aims to demonstrate the energy savings enabled by the use of SCHC on a cellular IoT network by the means of real-life implementation and measurements. Experiments are conducted in a controlled environment for different scenarios and considering multiple parameters such as message size and radio conditions. Measurements show the high impact of this header compression mechanism, particularly when the radio conditions are bad and repetitions are used to improve the reliability of the transmission: a reduction of up to 40% in energy consumption is observed. Using SCHC over the non-IP transport mode (NIDD) of NB-IoT compared to the legacy IP mode also enables significant energy savings and allows the latency to be reduced while maintaining the interoperability provided by the IP layer.