Ni–Ti–Hf shape memory alloys (SMAs) have shown great potential in high-temperature applications, including those in aviation, space, actuators, and energy exploration. However, conventional machining of these difficult-to-machine materials can lead to issues such as degradation of shape memory properties, dimensional inaccuracy, and high tool wear. As a result, non-traditional machining processes are preferred, with Wire Electric Discharge Machining (WEDM) showing better results than other methods. A recent study investigated the effect of WEDM process parameters on the machining of Ni–Ti–Hf SMAs by implementing an RSM-based Central Composite Design (CCD) technique. The pulse time was found to be the most influential parameter for cutting rate (MRR) and surface roughness (SR). The study also aimed to build a prediction model using Artificial Neural Network (ANN) for the most critical WEDM control parameters, namely CR and SR, with an error below 5%. Additionally, the surface integrity of the machined samples was examined using SEM, EDS, and microhardness. The results revealed that surface defects like micro-cracks and micro-pores increased with an increase in discharge energy, and a harder surface was observed near the machined zone. The minimum and maximum Recast Layer Thickness (RLT) obtained were 9.27 and 49.14 µm, respectively.