Machine for making espresso coffee of the type comprising at least one delivery unit provided with an attachment for a delivery cup and with a driving device provided with a lever movable from a first lever position to a second lever position, wherein the delivery unit comprises a first cylinder inside which a first piston is mounted in a slidable way which is movable by means of the lever from a first initial position of the first piston to a second position of the first piston and wherein the driving device is provided with return means of the lever from the second lever position to the first lever position, the delivery unit being connected to a hydraulic circuit of the machine in such a way that the movement of the first piston from the first position to the second position causes the charging of hot water within a housing of the first cylinder and in such a way that the movement of the first piston from the second position to the first position causes the discharging of the hot water from the housing of the first cylinder towards the delivery cup wherein the delivery unit comprises at least one braking device (6, 6', 6"), the braking device (6, 6', 6") being configured in such a way as to exert a braking force on the driving device of the delivery unit at least during the movement of the first piston from the second position of the first piston to the first position of the first piston, the braking force braking at least the lever at least during the movement of the lever from the second lever position to the first lever position, characterised in that said braking device (6, 6', 6") comprises a second internally hollow cylinder with a circuit independent of the first cylinder, the second cylinder being provided with a cavity filled with a fluid, a second piston (8, 8', 8") being mounted in a slidable way within the cavity, the second piston (8, 8', 8") being connected to the delivery unit according to a configuration in which said second piston (8, 8', 8") is movable by means of the lever between a first position and a second position, said second piston (8, 8', 8") separating two chambers (21, 22) internal to said cavity of which a first chamber and a second chamber which are separated from each other by the movable interposition of the second piston (8, 8', 8") which, following the sliding movement within the cavity, causes a variation of the volume of the first chamber and of the second chamber and causes a passage of the fluid contained in the cavity between the first chamber and the second chamber, the passage of the contained fluid between the first chamber and the second chamber occurring by means of passages (18, 19) in the form of through-openings obtained on the second piston (8, 8', 8") which put in communication with each other the first chamber and the second chamber, the braking device (6, 6', 6") being connected to the driving device according to a configuration in which: - the action of movement of the lever by the operator from the first lever position to the second lever position to start the phase of delivery of the coffee causes the charging of the one or more return means and causes the passage of the second piston (8, 8', 8") from the first position towards the second position in such a way as to apply an essentially null braking force during the movement of the lever from the first lever position to the second lever position; - the return of the lever from the second lever position to the first lever position, caused by the reaction of the one or more return means, causes the passage of the second piston (8, 8', 8") from the second position towards the first position in such a way as to exert the braking action on the lever. - the action of movement of the lever by the operator from the first lever position to the second lever position to start the phase of delivery of the coffee causes the charging of the one or more return means and causes the passage of the second piston (8, 8', 8") from the first position towards the second position in such a way as to apply an essentially null braking force during the movement of the lever from the first lever position to the second lever position; - the return of the lever from the second lever position to the first lever position, caused by the reaction of the one or more return means, causes the passage of the second piston (8, 8', 8") from the second position towards the first position in such a way as to exert the braking action on the lever.