Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, have been widely implemented during the COVID-19 pandemic. In addition to playing an important role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply and altering the strength of selection for novel variants. However, it is unclear how NPIs might affect the emergence of novel variants of concern that are able to escape pre-existing immunity (partially or fully), are more transmissible, or cause greater mortality. Here, we analyse a stochastic two-strain epidemiological model to determine how the strength of NPIs affects the emergence of variants with similar or contrasting life-history characteristics to the wildtype. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross immunity to have a greater probability of emerging at intermediate levels of NPIs. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be implementation of strong, timely NPIs.