The vulcanization properties, physicochemical, dielectric, and electrical properties of natural rubber-based composites were investigated and compared. The composites contain 30–70 phr functional fillers having low (silicon dioxide (SiO2)) and high (titanium dioxide (TiO2)) dielectric constant values. The possibilities of using the composites as substrates in compact flexible antennas have been evaluated. Fillers are also characterized. It has been shown that they have a noticeable but different influence on all the properties of the composites studied. That is primarily due to the different structure and specific properties of SiO2 and TiO2, thereby determining the different “filler–filler” and “rubber–filler” interactions. The composite filled with TiO2 at 70 phr has a better capacity to act as a substrate in body area network antennas than the SiO2-filled composites. An antenna with such a substrate has features that meet all the requirements of the industrial, science, and medical spectrum. TiO2 composites do not change their resistance to pressure or deflection within certain limits, having a self-cleaning and antibacterial effect, which is also beneficial for their usage in antennas that are left on or near the human body.