A plurality of contact elements, such as contact bumps or free-standing spring contacts including both monolithic and composite interconnection elements, are mounted to relatively small tile substrates which, in turn, are mounted and connected to a relatively large electronic component substrate, thereby populating the electronic component with a plurality of contact elements while avoiding the necessity of yielding the contact elements directly upon the electronic component. The relatively large electronic component is suitably a space transformer component of a probe card assembly. In this manner, pressure connections can be made to an entire semiconductor wafer, at once, to provide for wafer-level burn-in, and the like. Solder balls, z-axis conductive adhesive, or compliant connections are suitably employed for making electrical connections between the tile substrates and the electronic component. Multiple die sites on a semiconductor wafer are readily probed using the disclosed techniques, and the tiles can be arranged to optimize probing of an entire wafer. Composite interconnection elements having a relatively soft core overcoated by a relatively hard shell, as the resilient contact structures are described. Techniques for maintaining a prescribed x-y and z-axis alignment of the tiles to the relatively large substrate are disclosed.