Visible crew/equipment: After Senator Kelly's death, watch Storm as she runs away. On her right, a microphone wire is visible. (01:00:40)
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Suggested correction: Doesn't appear to be a wire, but rather a line in the fabric of the shirt she is wearing. There is one on the other side that you can see when she walks in to the room. Also, I don't think they wear microphones. Usually there is a boom mic overhead. You can see examples of the boom being used in the special features disc of X-Men 1.5 that shows you behind the scenes footage.
It is a battery pack for a mic. Bryan Singer admits this in the director's commentary.
