In this paper we apply robust optimization techniques to the problem of power control in mobile ad hoc wireless networks. Our approach is inherently multi-objective in that we seek a solution set that trades off the dual objectives of achieving optimality and maintaining feasibility. In particular, our objective is to minimize the aggregate power employed by the transmitters and the constraints are that the SINR at each receiver must exceed the threshold required for successful reception. The selection of the powers is complicated, however, by the fact that the channels incorporate random and unknown fading and attenuation components. A robust optimization framework for this problem is developed that penalizes the expected infeasibility of the proposed solution. The "cost of uncertainty" is measured by the total additional power required when all channel states are known. Our results demonstrate that communication dependability is enhanced through the robust formulation.