A micromechanical pumping system is formed on a substrate surface. The pumping system uses a pumping element which pumps a fluid through valves which move in a plane substantially parallel to the substrate surface. An electromagnetic actuating mechanism may also be fabricated on the surface of the substrate. Magnetic flux produced by a coil around a permeable core may be coupled to a permeable member affixed to a pumping element. The permeable member and pumping element may be configured to move in a plane parallel to the substrate. The electromagnetic actuating mechanism gives the pumping system a large throw and substantial force, such that the fluid pumped by the pumping system may be pumped through a transdermal cannula to deliver a therapeutic substance to the tissue underlying the skin of a patient.