Most published applications of the estimand framework have focused on superiority trials. However, non-inferiority trials present specific challenges compared to superiority trials. The International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use notes in their addendum on estimands and sensitivity analysis in clinical trials that there may be special considerations to the implementation of estimands in clinical trials with a non-inferiority objective yet provides little guidance. This paper discusses considerations that trial teams should make when defining estimands for a clinical trial with a non-inferiority objective. We discuss how the pre-addendum way of establishing non-inferiority can be embraced by the estimand framework including a discussion of the role of the Per Protocol analysis set. We examine what clinical questions of interest can be formulated in the context of non-inferiority trials and outline why we do not think it is sensible to describe an estimand as 'conservative'. The impact of the estimand framework on key considerations in non-inferiority trials such as whether trials should have more than one primary estimand, the choice of non-inferiority margin, assay sensitivity, switching from non-inferiority to superiority and estimation are discussed. We conclude by providing a list of recommendations, and important considerations for defining estimands for trials with a non-inferiority objective.