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Ultra-wideband (UWB) radar sensors are attracting more and more attention, e.g., for biomedical applications. In contrast to established techniques like X-ray tomography or invasive diagnostic approaches, UWB radar offers the potential for remote access and ultra-low power signal intensities. Inspired by promising studies of breast tumor imaging, we are continuing and extending our previous work on biomedical M-sequence radar and antenna techniques. We describe the development and the potential of innovative double-ridged horn antennas, based on high-permittivity sintered ceramics, which have been adapted to the envisaged biomedical applications. In this context, the miniaturization of UWB antennas, due to the restriction to small examination areas, without compromising the electromagnetic fidelity is the overall challenge. For the dielectric scaling of antennas with the potential to operate over wide bandwidths, we focus on nearly frequency independent, high-permittivity and low-loss materials. In what follows, we describe the arduous path from the first idea to functional laboratory versions of double-ridged horn antennas based on solid sintered ceramics. In this way, the paper illustrates the successful interdependence between microwave engineering and mechanical and material engineering.