The power characteristics of System-on-chips (SoCs) in nanoscale technologies are significantly impacted by process variations, making it important to consider these effects during system-level power analysis and optimization. In this paper, we identify and address the problem of designing effective power management schemes in the presence of such variations. In particular, we demonstrate that conventional power management schemes, which are designed without considering the impact of variations, can result in substantial power wastage. We therefore propose two approaches to variation-aware power management, namely, design-specific and chip-specific approaches. In each of these approaches, the goal is to consider the impact of variations while deriving the values of parameters that govern popular power management policies. The policy parameters are derived so as to optimize metrics that are relevant under variations. We motivate and introduce these metrics, and use a combination of analytical and empirical approaches to optimize them. We experimentally evaluate the proposed ideas in the context of an ARM processor core, and demonstrate that variation-aware power management can result in improvements of upto 59 % in mu + sigma of the energy distribution, and upto 55 % for the 95 percentile of the energy distribution, with respect to conventional power management schemes that do not consider variations.