Electromagnetic interference (EMI) shields and methods for broadband EMI shielding are provided. An EMI shield disposed in a path of electromagnetic radiation blocks a broad range of frequencies (>about 800 MHz to to 20 dB, while transmitting wavelengths in a visible range to an average transmission efficiency of >about 85% through the electromagnetic shield. The shield includes a flexible stack comprising a continuous ultrathin metal film comprising silver (Ag) and copper (Cu) and two antireflection dielectric layers disposed on either side of the ultrathin metal film. The shield may also include multiple stacks or an optional graphene layer that may be spaced apart from the flexible stack to achieve radiofrequency (RE) absorption, which provides additional form of EMI shielding. The EMI shield can be made via roll-to-roll sputtering.