A method of making espresso and a portable espresso machine incorporating that method that is compact, lightweight, requires low power, and is readily transportable. The quantity of water required to make espresso is heated to the brewing temperature in a boiler equipped with a piston. The piston is driven by an electric motor. During the brewing cycle, the hot water is pushed by the piston through the compacted coffee contained in the portafilter. The rate of piston movement is chosen such that the coffee in the portafilter is infused by the hot water at the high pressure necessary for making espresso, typically about 100 psi or higher, and also such that the contact between the coffee and water is of a duration suitable for making espresso, typically about 15-25 seconds. The components are thermally insulated and strategically placed to minimize the size of the machine and allow for portability.