Precise machining of micro parts from difficult-to-cut materials requires using advanced technology such as wire electrical discharge machining (WEDM). In order to enhance the productivity of micro WEDM, the key role is understanding the influence of process parameters on the surface topography and the material’s removal rate (MRR). Furthermore, effective models which allow us to predict the influence of the parameters of micro-WEDM on the qualitative effects of the process are required. This paper influences the discharge energy, time interval, and wire speed on the surface topography’s properties, namely Sa, Sk, Spk, Svk, and MRR, after micro-WEDM of Inconel 718 were described. Developed RSM and ANN model of the micro-WEDM process, showing that the discharge energy had the main influence (over 70%) on the surface topography’s parameters. However, for MRR, the time interval was also significant. Furthermore, a reduction in wire speed can lead to a decrease in the cost process and have a positive influence on the environment and sustainability of the process. Evaluation of developed prediction models of micro-WEDM of Inconel 718 indicates that ANN had a lower value for the relative error compared with the RSM models and did not exceed 4%.