We discuss the analysis of non‐inferiority trials based on a multi‐armed design with multiple correlated endpoints. We consider five different scenarios: (1) global non‐inferiority; (2) non‐inferiority for subsets of comparisons; (3) global non‐inferiority for a treatment group; (4) global non‐inferiority for an endpoint; and (5) local non‐inferiority. We describe and compare related approaches, which are based on the union‐intersection and intersection‐union test principles – alone and in combination. Because non‐inferiority thresholds for many differently scaled endpoints are rarely available in practice, the approaches described focus on the estimation of simultaneous confidence limits and their post hoc interpretation on non‐inferiority. We discuss and demonstrate pros and cons by means of a real data example. Copyright © 2012 John Wiley & Sons, Ltd.