In this paper we present a statistical method for estimating the maximum power consumption in VLSI circuits. The method is based on the theory of extreme order statistics applied to the probabilistic distribution of the cycle-based power consumption, maximum likelihood estimation, and Monte-Carlo simulation. The method can predict the maximum power in the constrained space of given input vector pairs as well as the complete space of all possible input vector pairs. The simulation-based nature of the proposed method allows one to avoid the limitations imposed by simple gate-level delay models and handle arbitrary circuit structures. The proposed method can produce maximum power estimates to satisJL user-specified error and confidence levels. Experimental results show that this method provides maximum power estimates within 5% of the actual value and with a 90% confidence level by simulating, on average, about 2.500 vector pairs.