An ear cup with a microphone apparatus which comprises an inner cup portion (1),for forming a noise damping space, and an outer cup portion (2) for forming a space. for accommodating electronics and/or a current source. The inner cup portion(1) and the outer cup portion are separated by a partition. The inner cup portion(1) has a pocket and two opposingly located recesses in which a bracket for a microphone(7) is disposed. Over the microphone (7), a windshield is provided, this protectingthe microphone from being damaged and also damping wind noise. The windshieldhas an outer configuration that may be seen as a continuation of the outer cup portion(2), in order to prevent turbulence in the region of the windshield. The windshieldis produced from a porous material, which is surrounded by a mounting frame (16)having nap catches (17) for engagement in snap catches (18).