A flexible, foldable EM barrier attenuates electromagnetic radiation by at least 20 dB from 1 GHz to 30 GHz. The barrier includes an LF layer that blocks EM radiation at least at low frequencies, laminated to a textile support layer that reduces stress cracking of the LF layer and prevents widening of any cracks that do form. Embodiments further include an HF layer that blocks EM radiation at high frequencies, such as a metallized polymer film and/or an elastomer layer filled with conductive particles. The LF layer can be foil, mesh, or electroless metallization of the support textile or of another textile. A thermal insulation layer can be included. A topcoat can block UV, and primer layers can resist moisture. Barriers can be joined to each other and/or to adjacent structures by lanyards, webbing, sewing, soft connections, and/or flex joints formed by adhesively attached metallized textiles or films.