In this work, we propose a new paradigm called power emulation, which exploits hardware acceleration to drastically speedup power estimation. Power emulation is based on the observation that most power estimation tools typically perform the following sequence of operations: simulating the circuit to obtain value traces or statistics for the inputs of its constituent components, evaluating power models for each circuit component based on the input values seen during simulation, and aggregating the power consumption of individual components to compute the circuit's power consumption. We further recognize that the steps involved in power estimation (power model evaluation, aggregation) can themselves be thought of as synthesizable functions and implemented as hardware circuits. Thus, any given design can be enhanced by adding to it "power estimation hardware", and the resulting power model enhanced circuit can be mapped onto a hardware prototyping platform. While drastic speedups in power estimation (orders of magnitude) are possible using this approach, a significant challenge arises due to the increase in circuit size as a result of adding power estimation hardware. We propose a systematic methodology to reduce the size of the power model enhanced circuit through a suite of techniques, including power model reuse across different circuit components, regulating the granularity of components for power modeling, exploiting inter-component power correlations, resource sharing for power model computations, and the use of block memories for efficient storage within power models. We demonstrate the benefits of the proposed power emulation paradigm by applying it to register-transfer level (RTL) power estimation for industrial designs, resulting in speedups from around 10X to over 500X compared to state-of-the-art commercial power estimation tools.