The identification of valid surrogate markers of disease or disease progression has the potential to decrease the length and costs of future studies. Most available methods that assess the value of a surrogate marker ignore the fact that surrogates are often measured with error. Failing to adjust for measurement error can erroneously identify a useful surrogate marker as not useful or vice versa. We investigate and propose robust methods to correct for the effect of measurement error when evaluating a surrogate marker using multiple estimators developed for parametric and nonparametric estimates of the proportion of treatment effect explained by the surrogate marker. In addition, we quantify the attenuation bias induced by measurement error and develop inference procedures to allow for variance and confidence interval estimation. Through a simulation study, we show that our proposed estimators correct for measurement error in the surrogate marker and that our inference procedures perform well in finite samples. We illustrate these methods by examining a potential surrogate marker that is measured with error, hemoglobin A1c, using data from the Diabetes Prevention Program clinical trial.