To ensure meaningful comparison of test scores across groups or time, measurement invariance (i.e., invariance of the general factor structure and the values of the measurement parameters) across groups or time must be examined. However, many empirical examinations of measurement invariance of psychological/educational questionnaires need to address two issues: Using the appropriate model for ordinal variables (e.g., Likert scale items), and handling missing data. In two Monte Carlo simulations, this study examined the performance of one full-information-maximum-likelihood-based method and five multiple-imputation-based methods to obtain tests of measurement invariance across groups for ordinal variables that have missing data. Our results indicate that the full-information-maximum-likelihood-based method and one of the multiple-imputation-based methods generally have better performance than the other examined methods, though they also have their own limitations.