Value engineering (VE) and function analysis (FA) are technological tools for the functional enhancement and cost reduction of engineering projects. They also help to overcome mental inertia by acknowledging the voice of the customer in complicated systems. Antenna engineering, providing electromagnetic remote links, is an important area in engineering science, with a large number of innovative concepts. However, managing innovative ideas to improve performance, reliability, quality, safety, and reduce life cycle costs, is still a work in progress. This research was designed to apply VE and FA as frameworks for innovative ideas in antenna systems, especially with regard to imaging and radar systems. FA diagrams free a designers' mind from tools to instead focus on purpose, which can help them to obtain better ideas for solutions to problems. It was identified that there were several options available for functionality enhancement and cost reduction. The required functionalities of the components of antenna systems, and their advantages and limitations were indicated. In addition, it was identified that some of the advantages and limitations appeared for combinations of the components. Alternative methods for applications, such as polarization conversion and the separation of outgoing and incoming electromagnetic waves, were studied. Circular polarization (CP) is important for two-way communication, since left-handed circularly polarized waves usually return with right-handed CP from targets. Therefore, various methods for producing CP were discussed, such as metamaterial-based linear to circular polarization converters and waveguide polarizers. Also, potential extra applications for these systems were explained. Two examples were: (1) merging multiple systems with different operating frequencies using multiband components; and (2) applying a feeding system for multiple reflectors using surfaces that reflect half of the wave and transmit the other half. Consequently, it was identified that the clearance of existing functions, prioritization of customers, identification of system bottlenecks requiring innovative methods, and better communication between users and designers, were the key benefits of VE and FA.