To investigate the association between a continuous exposure and an outcome it is common to categorize the exposure and estimate the relative associations between categories. Error in measurement of the continuous exposure results in misclassification when the exposure is categorized. In this paper we investigate methods for correcting for this misclassification. We consider applications of methods for continuous exposures and for fundamentally categorical exposures. A particular challenge is that even nondifferential error in the underlying continuous exposure can result in differential misclassification in the categorized exposure, i.e. misclassification dependent on the outcome. For continuous exposures, there exist a range of methods for correcting for the effects of exposure measurement error on the exposure-outcome association, including regression calibration (RC), multiple imputation (MI), moment reconstruction (MR) and simulation extrapolation (SIMEX). There are also correction methods for use with genuinely categorical exposures, using estimated misclassification probabilities. Alongside simple methods using estimated misclassification probabilities, we also consider two RC based methods, MI and MR of the continuous exposure followed by categorization, and a new SIMEX method. Simulation studies are used to compare the methods when the true exposure is available in a validation study and the more common situation in which replicate or additional error-prone exposure measurements are available in a subsample. We restrict attention to the case where the underlying association between the continuous exposure and the outcome is linear on the appropriate scale. RC and SIMEX methods fail to correct adequately for bias. However, MI and MR perform well. Methods using estimated misclassification probabilities also perform well, provided differential misclassification is assumed, however these methods are restricted to estimation of odds ratios and have other practical drawbacks. MI and MR have the benefit of being flexible for use with different analysis models, with quantile-based cutpoints, and more easily accommodate covariate adjustment. In summary, we found that MI and MR can be applied to correct exposure-outcome associations for the effects of misclassification error when the association is linear. Extending MI and MR for use with categorized continuous exposures under nonlinear exposure-outcome associations is now an important area for further research.