The 3Cat-4 mission aims at demonstrating the capabilities of a CubeSat to perform Earth Observation (EO) by integrating a combined GNSS-R and Microwave Radiometer payload into a 1-Unit CubeSat. One of the greatest challenges is the design of an antenna that respects the 1-Unit CubeSat envelope while operating at the different frequency bands: Global Positioning System (GPS) L1 and Galileo E1 band (1575 MHz), GPS L2 band (1227 MHz), and the microwave radiometry band (1400–1427 MHz). Moreover, it requires between 8 and 12 dB of directivity depending on the band whilst providing at least 10 dB of front-to-back lobe ratio in L1 and L2 GPS bands. After a trade-off analysis on the type of antenna that could be used, a helix antenna was found to be the most suitable option to comply with the requirements, since it can be stowed during launch and deployed once in orbit. This article presents the antenna design from a radiation performance point of view starting with a theoretical analysis, then presenting the numerical simulations, the measurements in an Engineering Model (EM), and finally the final design and performance of the Flight Model (FM).