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This paper investigates marine heatwave (MHW) characteristics in New Zealand's Earth System Model (NZESM) simulations for present-day conditions and how they are projected to change in the future in relation to anthropogenic greenhouse gas emissions. Three emission scenarios following the state of the art shared-socioeconomic pathways (SSPs, SSP1 2.6, SSP2 4.5, and SSP3 7.0) are each evaluated with a set of three ensemble members. These analyses are focused on the ocean around New Zealand, where NZESM captures boundary currents and mesoscale eddies, due to its high-resolution nested ocean grid. For present-day conditions, the model overestimates MHW intensity and underestimates the number of annual MHW days for subtropical waters, while some smaller positive biases are present in subantarctic waters compared to observations. Despite this, NZESM agrees with the observational pattern that more intense MHWs and more annual MHW days are found in subtropical waters compared to subantarctic waters. NZESM projects that MHW intensity will increase more strongly in subtropical waters compared to subantarctic waters, while the largest changes in annual MHW days are projected south of Australia and the Tasman Sea in the Subtropical Front (STF) frontal region, which suggests a southward shift of the STF under increased greenhouse gas emissions. Results using a high-emission scenario (SSP3 7.0) show an increase between 80 and 100% of median MHW intensities by the end of the century relative to the present-day for all analyzed coastal regions, and MHW conditions could become permanent year-round by the end of the century.