An electronic module, and method for making same, includes free-formed, self-supported interconnect pillars that electrically connect cover electronic components disposed on a cover substrate with base electronic components disposed on a base substrate. The free-formed, self-supported interconnect pillars may extend vertically in a straight path between the cover electronic components and the base electronic components. The free-formed, self-supported interconnect pillars may be formed from an electrically conductive filament provided by an additive manufacturing process. By free-forming the self-supported interconnect pillars directly on the electronic components, the flexibility of electronic module design may be enhanced, while reducing the complexity and cost to manufacture such electronic modules.