An electrical connector includes a body and two or more electrical contacts. The body has a guide member that is elongated between a first end and a second end along a first axis and has a connector block at the first end. The connector has a very low profile (preferably, less than about 10 mm high), and the bottom of the body is surface-mountable on a circuit board. The height of the connector can be defined by a vertical axis perpendicular to the first axis. The connector block retains the contacts, which are spaced from one another in the direction of the first axis. The body also has a camming element that, in response to a force of a mating connector being moved along the first axis, brings the contacts of the connector and mating connector together in a generally vertical direction. The camming element may have two oppositely inclined ramp sections. When a mating connector having complementary contacts is, guided by the guide member, moved into engagement with the camming element, the first ramp lifts the mating connector, including its contacts, above the connector block, and the second ramp lowers the mating connector onto the connector block, with the contacts of the mating connector lowering onto and making contact with the contacts of the electrical connector. The camming motion minimizes wiping between the mating contacts and largely confines the relative motion of the contacts to a vertical direction. The contacts may be arrayed in two or more rows.