I have taken a similar approach to
@gills however with mine I made the blanking cover out of 0.5 mm black polypropylene (like the material that plastic ring binders are made from), this meant that I could fold the top and bottom over the sides of the grille. With the bits that are folded over the top and bottom I cut v shapes out of it so that the curved profile of the grille could be maintained. I then attached these folded over tabs with some 3M VHB tape to stop it being able to get pulled off the car and to keep it looking smooth. This material that I have used has a similar textured finish to what the lower plastic trim has. It still doesn't exactly look OEM though but does seem to be pretty effective.
I am sure that there would be a way of fitting something stronger from behind like the blanking plate that the FSI's have where the charge cooler is on the TDI cars however that was beyond my creativity and materials that I had in the garage.