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This paper investigates the robustness of two well-known applications of second-order consensus dynamics, namely mechanical and power networks. For uniform subsystem parameters, we derive expressions for the H∞norms of mechanical and power networks, from external disturbances to body displacements and to generator phase angles, respectively. The closed-form expressions are in terms of the physical parameters (damping coefficients and inertias) of the dynamics and in terms of the spectrum of the grounded Laplacian matrix associated with the network. We then analyze the dependence of the H∞norm of each network on both the network structure and the physical parameters. For a fixed network topology, we find that each system norm can be minimized by choosing the damping coefficient within a specified range. Theoretical contributions are verified via two illustrative examples for mechanical and power networks, in which we show that the network structure, number of the reference nodes and their location in the network can have considerable effects on the system H∞norm.