Near-percolated CNT-polymer composites are promising high-permittivity materials. The main challenge in the field consists of finding compromises that allow high permittivity and low losses in frequency ranges of interest. Using an emulsion approach and optimizing the size of the droplets and the curing procedure, we obtain unprecedented performances and measure giant permittivity larger than 20 000 at 100 Hz along with a conductivity below 10(-4) S/m.