Empirical peer effects research often employs censored peer data. Individuals may list only a fixed number of links, implying mismeasured peer variables. I first document that censoring is widespread in network data. I then introduce an estimator and characterize its inconsistency analytically; an assumption on the ordering of peers implies that censoring causes attenuated peer effects estimates. Next, I demonstrate the effect of censoring in two data sets, showing that estimates with censored data underestimate peer influence. I discuss interpretation of estimates, propose methods for correction and bounding, and give implications for the design of network surveys.