Basal melting beneath Antarctic ice shelves drives ice-shelf thinning, impacts buttressing of inland ice streams, and contributes to grounding line retreat, thus affecting the rate of global sea-level rise. Yet, processes controlling the spatial variability of basal melt remain poorly constrained because observations of the evolving basal topography are sparse. One important but poorly understood feature are basal terraces. Here, we present a ground-penetrating radar (GPR) dataset imaging the evolution of basal terraces in the cold-water cavity beneath Ekström Ice Shelf. The quasi three-dimensional GPR data are complemented by an autonomous phase-sensitive radio echo sounder (ApRES) record and airborne radar data. No significant changes in the basal topography are observed between the two field seasons. Basal melt rates at the terrace roofs are less than a meter per year and lower than the regional average, ApRES-derived monthly variability ranges between 0.3 and 0.6 m a^-1. A weak off-angle reflector suggests that melt rates at the terrace walls may be higher, but not higher than 4 m a^-1. Overall, basal terracing occurs predominantly near the grounding zone, and the ice-ocean interface becomes smooth further offshore. We conclude that basal terraces occur beneath both warm- and cold-cavity ice shelves and that the low melt rates at terrace roofs are consistent with previous studies suggesting that a stratified ocean layer shields the ice base from oceanic heat transport. However, melt rates at the terrace walls are also low. Therefore, our results suggest that once basal terraces are created near the grounding zone, they may enter a stagnant mode and subsequently advect with the ice-shelf flow towards the ice edge where they eventually disappear.