An interposer includes a substrate, first and second sets of contact pads carried by the substrate, and receptacles formed in a surface of the substrate and exposing contact pads of the second set. The interposer may also include conductive traces carried by the substrate to electrically connect corresponding contact pads of the first and second sets. The receptacles are configured to at least partially receive conductive structures, such as solder balls, that are secured to the contact pads of the second set. Thus, the interposer is useful in providing semiconductor device assemblies and packages of reduced height or profile. Such assemblies and packages are also described, as are multi-chip modules including such assemblies or packages. In addition, methods for designing and fabricating the interposer are disclosed, as are methods for forming assemblies, packages, and multi-chip modules that include the interposer.