A rerouting element for a semiconductor device includes a dielectric film that carries conductive vias, conductive elements, and contact pads. The conductive vias are positioned at locations that correspond to the locations of bond pads of a semiconductor device with which the rerouting element is to be used. The conductive elements, which communicate with corresponding conductive vias, reroute the bond pad locations to corresponding contact pad locations adjacent to one peripheral edge or two adjacent peripheral edges of the rerouted semiconductor device. The rerouting element is particularly useful for rerouting centrally located bond pads of a semiconductor device, as well as for rerouting the peripheral locations of bond pads of a semiconductor device to one or two adjacent peripheral edges thereof. Methods for designing and using the rerouting element are also disclosed, as are semiconductor device assemblies including one or more rerouting elements.