We describe a technology in which multiple components inside a circuit pack shielded from electromagnetic interference (EMI) are efficiently cooled by individual heat sinks that protrude into an external airflow through openings in the lid of the shield. Compliant, electrically conductive gaskets are used to form perimeter seals between the bases of the heat sinks and the lid of the enclosure. The gaskets accommodate variations in the heights of the components and allow solid-to-solid contact in the thermal-grease-filled interface between the components and their heat sinks without compromising EMI shielding. This technology provides efficient cooling because the heat sinks can be tailored to the thermal loads of the individual components. Moreover, a set of small heat sinks presents a lower flow resistance to the cooling airflow than the conventional configuration of fins covering the entire lid of an EMI shield. We have examined the implementation of this solution by numerical modeling and by experiment. It leads to acceptable thermal performance, and lower flow resistance relative to the conventional approach. It may reduce cost and weight and it eases rework.