Most epidemiological studies suffer from misclassification in the response and/or the covariates. Since ignoring misclassification induces bias on the parameter estimates, correction for such errors is important. For measurement error, the continuous analog to misclassification, a general approach for bias correction is the SIMEX (simulation extrapolation) method. This approach has been recently extended to regression models with a possibly misclassified categorical response and/or the covariates and is called the MC-SIMEX approach. In order to assess the importance of a regressor not only its (corrected) estimate is needed, but also its standard error. Based on the original SIMEX approach a method which uses asymptotic expansions to estimate the asymptotic variance is developed. The asymptotic variance estimators for the MC-SIMEX approach are derived. The case when the misclassification probabilities are estimated by a validation study is also included. An extensive simulation study shows the good performance of the new approach. It is illustrated by an example in caries research including a logistic regression model, where the response and a binary covariate are possibly misclassified.