Surveys often yield estimates that are suspected to be biased, because of either non-response bias and/or measurement error. Numerous methods exist for eliminating non-response bias (e.g., re-weighting the data, individual-level models of selection, or deriving bounds on the true population parameter). But in many settings these methods may not be tractable or helpful, and usually ignore measurement error. I propose a method for dealing with both non-response bias and measurement error simultaneously, when using surveys to estimate rates or proportions. The method exploits `auxiliary information’ from analogous surveys, where it is possible to derive the relative amount of non-response bias and measurement error. I demonstrate the method in the case of voter turnout, where a reasonably large body of vote validation studies supply auxiliary information, allowing the components of bias in survey estimates of turnout rates to be isolated. Averaging over the auxiliary information provides bounds on the quantity of interest, yielding an estimate corrected for both non-response bias and measurement error.