The calculation results of the influence of contact resistances of the metal-semiconductor interface on the output power of a flexible microthermoelectric generator is presented. The calculation method based on semiconductor theory. The contact area of the conductor (metal) and thermoelectric material (semiconductor) is characterized by a discrepancy between bulk properties and irregularities in a thin area near the interface. Different thermal and electrical carriers (phonons and electrons) encounter different resistances in this interface area. The calculations were carried out using ANSYS Workbench and Wolfram Mathematica. Output power simulation was carried out by taking into account contact electric and thermal resistances influence on the metal–semiconductor interface for six contact couples (three metals, two semiconductors). Interface contact resistances significantly reduce the output power. It was shown that contact resistances reduce the output power of the thermoelectric device by 64–70% depending on the metal type of the metal–semiconductor contact couple. The presented results of calculating interface contact resistances correspond to experimental measurements in references, which allows us to conclude that this method of calculating interface electrical and thermal contact resistances can be used in the case of microelectronic fabrication of thermoelectric devices.