The limited energy resources in portable multimedia devices require the reduction of encoding complexity. The complex Motion Estimation (ME) scheme of H.264/MPEG-4 AVC accounts for a major part of the encoder energy . In this paper we present a Run-Time Adaptive Predictive Energy Budgeting (enBudget) scheme for energy-aware ME that predicts the energy budget for different video frames and different Macroblocks (MBs) in an adaptive manner considering the run-time changing scenarios of available energy, video frame characteristics, and user-defined coding constraints while keeping a good video quality. It assigns different Energy-Quality Classes to different video frames and fine-tunes at MB level depending upon the predictive energy quota in order to cope with above-mentioned run-time unpredictable scenarios. Compared to UMHexagonS , EPZS , and FastME , our enBudget scheme for energy-aware ME achieves an energy saving of up to 93%, 90%, 88% (average 88%, 77%, 66%), respectively. It suffers from an average Peak Signal to Noise Ratio (PSNR) loss of 0.29 dB compared to Full Search. We also demonstrate that enBudget is equally beneficial to various other state-of-the-art fast adaptive MEs (e.g. ). We have evaluated our scheme for ASIC and various FPGAs.