In electrical discharge machining (EDM), the machined surface quality can be affected by the excessive temperature generation during the machining process. To achieve a longer life of the finished part, the machined surface quality plays a key role in maintaining its overall integrity. Surface roughness is an important quality evaluation of a material’s surface that has considerable influence on mechanical performance of the material. Herein, a sintered cermet tooltip with 75% copper and 25% titanium carbide was used as tool electrode for processing H13 steel. The experiments have been performed to investigate the effects of EDM parameters on the machined surface roughness. The findings show that, as the pulse current, pulse length, and pulse interval are increased, the surface roughness tends to rise. The most significant determinant for surface roughness was found to be pulse current. A semi-empirical surface roughness model was created using the characteristics of the EDM technique. Buckingham’s theorem was used to develop a semi-empirical surface roughness prediction model. The semi-empirical model’s predictions were in good agreement with the experimental studies, and the built empirical model based on physical features of the cermet tooltip was tested using dimensional analysis.