A method for making and dispensing coffee-based beverages in machines includes increasing the water temperature inside a boiler and assembly to achieve preheating with to adjust the delivered thermal power. The method includes three dispensing steps. Preheated water at a selected temperature achieves a pre-infusion in a preset time or water volume without pressure in the hydraulic pump, wherein the coffee powder is only wet. Next, the coffee powder is infused by means of the use of a logic unit that manages the volume of dispensed water by a volumetric meter and at a preset, constant pressure as a function of the ground coffee and dispensed product weight. An amount by volume of water is dispensed and calculated to achieve a selected and preset brew ratio. Finally, post-infusion is achieved in which the hydraulic pump is deactivated for a time needed to reach by weight the programmed dose of dispensed product.