This paper explores the feasibility of and challenges in developing methods for black-box monitoring of a VM's power usage at runtime, on shared virtualized compute platforms, including those with complex memory hierarchies. We demonstrate that VM-level power utilization can be accurately estimated, or estimated with accuracy with bound error margins. The use of bounds permits more lightweight online monitoring of fewer events, while relaxing the fidelity of the estimates in a controlledmanner. Our methodology is evaluated on core i7 and core2 x86 platforms, running synthetic and SPEC benchmarks.