The present invention is directed toward clamping apparatus and methods for holding an item to an electrically conductive structure. In one embodiment, the clamp includes a strap, a fastener, a cushion, and a conductive material. The strap provides the structural strength for holding the item. The fastener is coupled to the strap for securing the strap to the structure. The cushion is disposed within the strap to at least partially isolate the item from shock and vibration transmitted through the strap. The conductive material is held by the cushioning material at least at a portion of the interior surface of the cushioning material. The conductive material is electrically coupled to the strap.