A common concern in non-inferiority (NI) trials is that non-adherence due, for example, to poor study conduct can make treatment arms artificially similar. Because intention-to-treat analyses can be anti-conservative in this situation, per-protocol analyses are sometimes recommended. However, such advice does not consider the estimands framework, nor the risk of bias from per-protocol analyses. We therefore sought to update the above guidance using the estimands framework, and compare estimators to improve on the performance of per-protocol analyses. We argue the main threat to validity of NI trials is the occurrence of "trial-specific" intercurrent events (IEs), that is, IEs which occur in a trial setting, but would not occur in practice. To guard against erroneous conclusions of non-inferiority, we suggest an estimand using a hypothetical strategy for trial-specific IEs should be employed, with handling of other non-trial-specific IEs chosen based on clinical considerations. We provide an overview of estimators that could be used to estimate a hypothetical estimand, including inverse probability weighting (IPW), and two instrumental variable approaches (one using an informative Bayesian prior on the effect of standard treatment, and one using a treatment-by-covariate interaction as an instrument). We compare them, using simulation in the setting of all-or-nothing compliance in two active treatment arms, and conclude both IPW and the instrumental variable method using a Bayesian prior are potentially useful approaches, with the choice between them depending on which assumptions are most plausible for a given trial.