An electromagnetically-shielded microelectronic assembly, comprising: first and second signal paths, which carry different electrical signals during operation of the microelectronic assembly; and an electromagnetic, EM, shield structure positioned between the first and second signal paths, the EM shield structure comprising: a magnetic shield portion having a first magnetic permeability and a first electrical conductivity; an electrical shield portion adjacent the magnetic shield portion, the electrical shield portion having a second magnetic permeability less than the first magnetic permeability and having a second electrical conductivity greater than the first electrical conductivity; the electromagnetically-shielded microelectronic assembly further comprising an assembly substrate having a frontside from which the EM shield structure projects, a first interconnect feature through which the first signal path extends, bonded to the substrate, and located on a first side of the EM shield structure and a second interconnect feature through which the second signal path extends, bonded to the substrate, and located on a second, opposing side of the EM shield structure; wherein the EM shield structure further comprises a dielectric substrate layer having a first principal surface and a second principal surface opposite the first principal surface; and wherein the magnetic shield portion comprises a magnetic shield layer in contact with the first principal surface, the electrical shield portion comprises an electrical shield layer in contact with the second principal surface of the dielectric substrate layer; and wherein the first interconnect feature comprises a bondwire bent into a curved shape, and wherein at least one of the magnetic shield layer and the electrical shield layer is patterned to have a planform geometry corresponding to the curved shape of the bondwire. first and second signal paths, which carry different electrical signals during operation of the microelectronic assembly; and an electromagnetic, EM, shield structure positioned between the first and second signal paths, the EM shield structure comprising: a magnetic shield portion having a first magnetic permeability and a first electrical conductivity; an electrical shield portion adjacent the magnetic shield portion, the electrical shield portion having a second magnetic permeability less than the first magnetic permeability and having a second electrical conductivity greater than the first electrical conductivity; the electromagnetically-shielded microelectronic assembly further comprising an assembly substrate having a frontside from which the EM shield structure projects, a first interconnect feature through which the first signal path extends, bonded to the substrate, and located on a first side of the EM shield structure and a second interconnect feature through which the second signal path extends, bonded to the substrate, and located on a second, opposing side of the EM shield structure; wherein the EM shield structure further comprises a dielectric substrate layer having a first principal surface and a second principal surface opposite the first principal surface; and wherein the magnetic shield portion comprises a magnetic shield layer in contact with the first principal surface, the electrical shield portion comprises an electrical shield layer in contact with the second principal surface of the dielectric substrate layer; and wherein the first interconnect feature comprises a bondwire bent into a curved shape, and wherein at least one of the magnetic shield layer and the electrical shield layer is patterned to have a planform geometry corresponding to the curved shape of the bondwire. a magnetic shield portion having a first magnetic permeability and a first electrical conductivity; an electrical shield portion adjacent the magnetic shield portion, the electrical shield portion having a second magnetic permeability less than the first magnetic permeability and having a second electrical conductivity greater than the first electrical conductivity; the electromagnetically-shielded microelectronic assembly further comprising an assembly substrate having a frontside from which the EM shield structure projects, a first interconnect feature through which the first signal path extends, bonded to the substrate, and located on a first side of the EM shield structure and a second interconnect feature through which the second signal path extends, bonded to the substrate, and located on a second, opposing side of the EM shield structure; wherein the EM shield structure further comprises a dielectric substrate layer having a first principal surface and a second principal surface opposite the first principal surface; and wherein the magnetic shield portion comprises a magnetic shield layer in contact with the first principal surface, the electrical shield portion comprises an electrical shield layer in contact with the second principal surface of the dielectric substrate layer; and wherein the first interconnect feature comprises a bondwire bent into a curved shape, and wherein at least one of the magnetic shield layer and the electrical shield layer is patterned to have a planform geometry corresponding to the curved shape of the bondwire.