Computer simulation is employed to simulate the electrodynamic parameters of new fractal antennas and frequency-selective surfaces based on such antennas in the frequency range up to 20 GHz. The analysis of the original fractal antennas is supplemented with the study of the fractal frequency-selective 3D media or fractal sandwiches (i.e., radioelectronic fractal micro/nanostructures that contain no less than two layers. The efficiency of the fractal antennas and the fractal frequency-selective 3D media is demonstrated. The methods to create new passive electron components and elements for modern broadband and multifrequency radio systems based on such media are proposed. These samples have been obtained within the framework of the new fundamental scientific direction “Fractal Radio Physics and Fractal Radio Electronics: Designing of the Fractal Radio Systems” which was suggested and is being developed in Kotelnikov IREE RAS by the author.