Motivated by possible applications in fault-tolerant routing, we introduce the notion of uniform mixed equilibria in network congestion games with adversarial link failures, where players need to route traffic from a source to a destination node. Given an integer rho >= 1, a rho-uniform mixed strategy is a mixed strategy in which a player plays exactly rho edge disjoint paths with uniform probabilities, so that a rho-uniform mixed equilibrium is a tuple of rho-uniform mixed strategies, one for each player, in which no player can lower her cost by deviating to another rho-uniform mixed strategy. For games with weighted players and affine latency functions, we show existence of rho-uniform mixed equilibria and provide a tight characterization of their price of anarchy. For games with unweighted players, instead, we extend the existential guarantee to any class of latency functions and, restricted to games with affine latencies, we derive a tight characterization of both the prices of anarchy and stability.