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Classical model-based diagnosis uses a model of the system to infer diagnoses – explanations – of a given abnormal observation. In this work, we explore how to address the case where there is uncertainty over a given observation. This can happen, for example, when the observations are collected by noisy sensors, that are known to return incorrect observations with some probability. We formally define this common scenario for consistency-based and abductive models. In addition, we analyze the complexity of two complete algorithms we propose for finding all diagnoses and correctly ranking them. Finally, we propose a third algorithm that returns the most probable diagnosis without finding all possible diagnoses. Experimental evaluation shows that this third algorithm can be very effective in cases where the number of faults is small and the uncertainty over the observations is not large. If, however, all possible diagnoses are desired, then the choice between the first two algorithms depends on whether the domain's diagnosis form is abductive or consistent.