Power and energy efficiency are among the most crucial requirements in high-performance and other computing platforms. This work examines through extensive experimentation methods and procedures suitable for assessing the power and energy efficiency of fundamental hardware building blocks inside a typical high-performance CPU, focusing on the dynamic branch predictor (DBP). The investigation relies on the Running Average Power Limit (RAPL) interface from Intel, a software tool for credibly reporting the power and energy based on instrumentation inside the CPU. We use well-known microbenchmarks under various run conditions to explore potential pitfalls and to develop precautions to raise the precision of the measurements obtained from RAPL for more reliable power estimation. The authors discuss the factors that affect measurements and share the difficulties encountered and the lessons learned.