ABS Plastic Sheet 1/8 Inch Thick, 2 Pack 12" x 16" x 3mm Black Moldable Thermoplastic Panel Smooth & Textured Finish High Tensile for DIY Crafts Car Interiors Home Decoration (Black, 12''×16'')

I used some thin plastic sheeting to back mine. Worked great as they actually already had a slim pocket on the back side, next to the main pouch that I could fit them in while keeping the main pocket un-obstructed. I wouldn't trust cardboard to last, and foam to be rigid enough.