Assessing the variability of an estimator is a key component of the process of statistical inference. In nonparametric regression, estimating observation-error variance is the principal ingredient needed to estimate the variance of the regres- sion mean. Although there is an extensive literature on variance estimation in nonparametric regression, the techniques developed in conventional settings gener- ally cannot be applied to the problem of regression with errors in variables, where the explanatory variables are not directly observable. In this paper we introduce methods for estimating observation-error variance in errors-in-variables regression. We consider cases where the variance is modelled either nonparametrically or para- metrically. The performance of our methods is assessed both numerically and the- oretically. We also suggest a fully data-driven bandwidth selection procedure, a problem that is notoriously difficult in errors-in-variables contexts.