In this paper, we present the Kepler framework, designed to address the critical need for precise power and energy measurement in on-prem cloud-native, containerized environments, with a specific focus on processes, containers, and Kubernetes pods. The framework aims to support other tools in making informed decisions regarding provisioning, scheduling, and energy-optimization in cloud environments. Our approach involves leveraging the Kepler framework to create power models using Hardware Counters (HC), and realtime system power metrics from hardware sensors like x86 Running Average Power Limit (RAPL). Unlike previous methods that create and validate power models using aggregated system metrics, we propose a versatile process-level power model trained with per-process metrics. Those metrics are collected via a series of experiments in a controlled environment, measuring the incremental power consumption of processes under different scenarios. The collected data is then utilized to create a power model to be used in a shared cloud environment, and to validate the created power models using different set of input metrics. Our results show a significant improvement in the model accuracy compared to prior works, when incorporating perprocess metrics and real-time system power metrics into the power estimation process. For instance, using the simplest power model, which is based on CPU utilization ratio, resulted in a Sum of Squared Error (SSE) of 75. In contrast, a power model created using aggregated system metrics, as the related works, had an SSE of 175 without real-time power metrics, and 5.6 with our proposed model refinement by normalizing the model results with the real-time system power metrics. On the other hand, training the power model with per-process metrics from controlled experiments yielded an SSE as low as 1.68 using realtime system power metrics, representing a 70% improvement in model accuracy compared to using aggregated system metrics, and an SSE 8.7 without power metrics, representing a 95% improvement in model accuracy. Furthermore, the results show that Kepler has a notable lower overhead by utilizing extended Berkeley Packet Filter (eBPF) for HC collection than alternative methods.