Microelectronic contact structures are fabricated by separately forming, then joining together, various components thereof. Each contact structure has three components: a “post” component, a “beam” component, and a “tip” component. The resulting contact structure, mounted to an electronic component, is useful for making an electrical connection with another electronic component. The post component can be, fabricated on a sacrificial substrate, joined to the electronic component and its sacrificial substrate removed. Alternatively, the post component can be formed on the electronic component. The beam and tip components can each be fabricated on a sacrificial substrate. The beam component is joined to the post component and its sacrificial substrate is removed, and the tip component is joined to the beam component and its sacrificial substrate is removed. In an embodiment of the invention, the beam components of adjacent contact structures are disposed at different heights above the electronic component, whereby at least a portion of the first beam component can overlap at least a portion of the second beam component, thereby conserving space required to accommodate the beam components on the surface of the electronic component.