A stabilizing apparatus for stabilizing the position of a needle when penetrating the skin of a patient, the apparatus has a frame structure with a base for placement against the skin in the vicinity of an intended needle entry point. A flexible diaphragm is supported by the frame structure and is spaced apart from the base of the frame structure to be disposed at a position away from the skin. The flexible diaphragm is configured to releasably grip the shaft of the needle at a distance from the needle entry point.
