While the use of networks to understand how complex systems respond to perturbations is pervasive across scientific disciplines, the uncertainty associated with estimates of pairwise interaction strengths (edge weights) remains rarely considered. Mischaracterizations of interaction strength can lead to qualitatively incorrect predictions regarding system responses as perturbations propagate through often counteracting direct and indirect effects. Here, we introduce PressPurt, a computational package for identifying the interactions whose strengths must be estimated most accurately in order to produce robust predictions of a network’s response to press perturbations. The package provides methods for calculating and visualizing these edge-specific sensitivities (tolerances) when uncertainty is associated to one or more edges according to a variety of different error distributions. The software requires the network to be represented as a numerical (quantitative or qualitative) Jacobian matrix evaluated at stable equilibrium.