A method of making an interposer having an array of contact structures for making temporary electrical contact with the leads of a chip package. The contact structures may make contact with the leads substantially as close as desired to the body of the chip package. Moreover, the contact structures can be adapted for making contact with leads having a very fine pitch. In a first embodiment, the contact structures include raised members formed over a body of the interposer. A conductive layer is formed over each of the raised members to provide a contact surface for engaging the leads of the chip package. In another embodiment, the raised members are replaced with depressions formed into the interposer. A conductive layer is formed on an inside surface of each depression to provide a contact surface for engaging the leads of the chip package. Moreover, any combination of raised members and depressions may be used.