An electric motor-driven compressor comprising: a housing assembly comprising a motor housing and a first compressor housing mounted to one end of the motor housing, the motor housing containing a motor stator and a motor rotor having a shaft, the motor housing defining a bore through which the motor rotor and the shaft pass; the first compressor housing containing a first centrifugal compressor wheel that is mounted on one end of the shaft for rotation therewith, the first compressor housing also defining a first compressor flow path including a first air inlet that leads air into the first compressor wheel, and a first volute that collects compressed air that has passed through and been compressed by the first compressor wheel; and the motor housing defining a convoluted liquid coolant passage therein, the coolant passage defining an inlet and an outlet respectively located proximate opposite axial ends of the motor housing, the coolant passage defining a plurality of axially spaced-apart, convoluted passageways arranged for serial flow of liquid coolant from the inlet, then through each of the convoluted passageways one after another, and finally out from the outlet, characterized in that: the coolant passage splits into two sets of convoluted passageways respectively having right-hand convolutions and left-hand convolutions, each of which convoluted passageways routes the liquid coolant through a series of reversals of flow direction about the motor housing axis, wherein coolant entering through the inlet splits into two portions, one flowing through the right-hand convolutions and the other flowing through the left-hand convolutions, wherein said coolant portions rejoin and exit through the outlet. a housing assembly comprising a motor housing and a first compressor housing mounted to one end of the motor housing, the motor housing containing a motor stator and a motor rotor having a shaft, the motor housing defining a bore through which the motor rotor and the shaft pass; the first compressor housing containing a first centrifugal compressor wheel that is mounted on one end of the shaft for rotation therewith, the first compressor housing also defining a first compressor flow path including a first air inlet that leads air into the first compressor wheel, and a first volute that collects compressed air that has passed through and been compressed by the first compressor wheel; and the motor housing defining a convoluted liquid coolant passage therein, the coolant passage defining an inlet and an outlet respectively located proximate opposite axial ends of the motor housing, the coolant passage defining a plurality of axially spaced-apart, convoluted passageways arranged for serial flow of liquid coolant from the inlet, then through each of the convoluted passageways one after another, and finally out from the outlet, characterized in that: the coolant passage splits into two sets of convoluted passageways respectively having right-hand convolutions and left-hand convolutions, each of which convoluted passageways routes the liquid coolant through a series of reversals of flow direction about the motor housing axis, wherein coolant entering through the inlet splits into two portions, one flowing through the right-hand convolutions and the other flowing through the left-hand convolutions, wherein said coolant portions rejoin and exit through the outlet.