There has been a renewed interest in applying multiobjective (MO) optimization methods to a number of problems in the physical sciences, including to rf structure design. The results of these optimizations generate large datasets, which makes visualizing the data and selecting individual solutions difficult. Using the generated results, Pareto fronts can be found giving the trade-off between different objectives, allowing one to utilize this key information in design decisions. Although various visualization techniques exist, it can be difficult to know which technique is appropriate and how to apply them successfully to the problem at hand. First, we present the setup and execution of MO optimizations of one standing wave and one traveling wave accelerating cavity, including constraint handling and an algorithm comparison. In order to understand the generated Pareto frontiers, we discuss several visualization techniques, applying them to the problem, and give the benefits and drawbacks of each. We found that the best techniques involve clustering the resulting data first to narrow down the possible choices and then using multidimensional visualization methods such as parallel coordinate plots and decision maps to view the clustered results and select individual solutions. Finally, we give some examples of the application of these methods and the cavities selected based on arbitrary design requirements.