The general task of network reliability analysis is this: given some probabilistic information about the possible failures of network components, we want to compute a global reliability metric for the network. This general task can take many different forms, depending on the specific reliability metric. Numerous methods are known to accomplish it in various situations, precisely or approximately, but usually demanding significant algorithmic complexity. The issue we address is that what happens if the input data is unreliable, i.e., it is only known with limited accuracy. We propose a mathematical approach that can estimate and bound the resulting error, in terms of the input inaccuracy. It is particularly interesting that the method applies to a very broad class of models, independently of the actual reliability model that is chosen from the class. This feature allows wide applicability of our method, and also makes possible the handling of uncertainties in the considered model itself, not only in the input data.