This paper presents a computationally simple and accurate method to compute the error probabilities in decentralized detection in sensor networks. The cost of the direct computation of these probabilities-e.g., the probability of false alarm, the probability of a miss, or the average error probability-is combinatorial in the number of sensors and becomes infeasible even with small size networks. The method is based on the theory of large deviations, in particular, the saddlepoint approximation and applies to generic parallel fusion sensor networks, including networks with nonidentical sensors, nonidentical observations, and unreliable communication links. The paper demonstrates with parallel fusion sensor network problems the accuracy of the saddlepoint methodology: 1) computing the detection performance for a variety of small and large sensor network scenarios; and 2) designing the local detection thresholds. Elsewhere, we have used the saddlepoint approximation to study tradeoffs among parameters for networks of arbitrary size