In battery applications, every electrical connection of battery cells is important because it influences functionality, efficiency, and safety. Increased contact resistances generate more heat at the affected terminals and if contact resistances of parallel-connected battery cells differ the current divides unequally. Amongst different techniques, detachable connections are easy to handle and have advantages for service, repair and recycling. Usually, detachable electrical connections are based on the functional principle of press contacts. So, press contacts are frequently used for consumer batteries in electronic devices, for pouch battery cells in scientific tests, and for large battery cells with screw connections. This paper focusses on the electrical contact resistance of press contacts for battery cells. A novel measuring method to assess the contact resistance itself is presented. Common terminal and connector metals for battery cells and the dependence of their contact resistances on the contact pressure, surface roughness, and contact area are investigated and compared with welding techniques. Only if these dependencies are considered, contact resistances as low as for welded connections are achieved. Furthermore, due to its hard passivating Al203 surface film, aluminum contacts need a certain surface roughness. The obtained results can serve for modeling and development of battery assemblies.