Disclosed is a high frequency attenuation core and cable. The core includes a conductor surrounded by a high frequency energy absorbing medium, then surrounded by a dielectric, and then surrounded by an outer layer made from a material having a high complex dielectric constant. The cable includes the above described core surrounded by an electromagnetic interference (EMI) shield which is further surrounded by a conductive layer. The cable and core as described above may be used in harness applications wherein a plurality of cores and/or cables as described above are surrounded by a gross shield. In addition, when the cores described above are used in multi-core applications, they may individually include an additional EMI shield for greater electromagnetic interference protection.