A pressure-sensor device comprising: - a pressure-sensitive component (5, 5a, 6; 5a, 5b, 5c, 6), having a sensor body (5; 5a, 5b, 5c) that includes an elastically deformable membrane part and at least one detection element suitable for detecting a deformation of the elastically deformable membrane part; - a housing or supporting structure (2, 3) for housing or supporting the pressure-sensitive component (5, 5a, 6; 5a, 5b, 5c, 6), having at least one passageway for a fluid of which a pressure is to be measured, the housing or supporting structure (2, 3) comprising: - a housing or supporting body, with respect to which the sensor body (5; 5a, 5b, 5c) is positioned in such a way that its elastically deformable membrane part is exposed to the fluid exiting the at least one passageway, the housing or supporting body having at least one through cavity; - at least one compressible element (20, 21), which is configured for compensating possible variations of volume of the fluid and delimits at least in part at least one respective duct for the fluid (20a, 21a; 20a', 21a') having an inlet end and an outlet end, wherein the housing or supporting body has a first body portion comprising a transverse wall of the through cavity in which at least one first passage (23a-23b) is defined; wherein the passageway for the fluid comprises said at least one duct (20a, 21a; 20a', 21a') and said at least one first passage (23a-23b); wherein the at least one first passage (23a-23b) has at least one respective inlet and at least one respective outlet, at least one of the at least one inlet and the at least one outlet being in fluid communication with the at least one duct (20a, 21a; 20a', 21a'), and wherein the at least one inlet and the at least one outlet of the at least one first passage (23a-23b) are arranged so as to define a tortuous path for the fluid, the at least one inlet and the at least one outlet being in particular arranged in positions staggered in a lateral direction, the pressure-sensor device being characterized in that the at least one inlet and the at least one outlet of the at least one first passage (23a-23b) comprise a first cavity and a second cavity each having a bottom, which are defined at opposite sides of the transverse wall and are formed so as to intersect each other in a lateral direction. - a pressure-sensitive component (5, 5a, 6; 5a, 5b, 5c, 6), having a sensor body (5; 5a, 5b, 5c) that includes an elastically deformable membrane part and at least one detection element suitable for detecting a deformation of the elastically deformable membrane part; - a housing or supporting structure (2, 3) for housing or supporting the pressure-sensitive component (5, 5a, 6; 5a, 5b, 5c, 6), having at least one passageway for a fluid of which a pressure is to be measured, the housing or supporting structure (2, 3) comprising: - a housing or supporting body, with respect to which the sensor body (5; 5a, 5b, 5c) is positioned in such a way that its elastically deformable membrane part is exposed to the fluid exiting the at least one passageway, the housing or supporting body having at least one through cavity; - at least one compressible element (20, 21), which is configured for compensating possible variations of volume of the fluid and delimits at least in part at least one respective duct for the fluid (20a, 21a; 20a', 21a') having an inlet end and an outlet end, - a housing or supporting body, with respect to which the sensor body (5; 5a, 5b, 5c) is positioned in such a way that its elastically deformable membrane part is exposed to the fluid exiting the at least one passageway, the housing or supporting body having at least one through cavity; - at least one compressible element (20, 21), which is configured for compensating possible variations of volume of the fluid and delimits at least in part at least one respective duct for the fluid (20a, 21a; 20a', 21a') having an inlet end and an outlet end,