Meta-analyses have become the gold standard for synthesizing evidence from multiple clinical trials. They are especially useful when clinical trials are small and the outcome is rare or adverse since individual trials often lack sufficient power to detect a treatment effect. However, when zero events are observed in one or both treatment arms in a trial, commonly used meta-analysis methods fail. Continuity corrections, numerical adjustments to the data to make computation feasible, have been proposed to ameliorate this issue, but the impact of the various available continuity corrections on meta-analyses with rare events has not been explored. We compare several continuity corrections via a simulation study with a variety of commonly used meta-analysis methods. We consider how these continuity corrections impact important meta-analysis results, such as the estimated overall treatment effect, estimated heterogeneity variance, and average Type I error rate.