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The evolution of ElectroMagnetic (EM) models and modern EM solvers permit resolving a variety of real-life EM propagation and radiation problems, in which antenna design and optimization account a large proportion. However, understanding of EM propagation processes on antenna structures and design achievements can be limited when only total antenna responses are considered and there is lacking of near-field analysis. This chapter provides a better insight into the EM propagation processes on traveling-wave antennas. A near-field propagation analysis method is proposed based on simulated near-field data with corresponding meshed structure data. This overcomes the insufficiencies and obstacles for observation of the conventional analysis methods. The EM-solver-run optimization and accurate sampling for field and structure data are the first important steps for the analysis. For general propagation problems such as paths recognition and characterization of the propagation, the EM signal models, impulse response analysis and super-resolution algorithms for Time of Arrival (ToA) estimation are studied and proposed. A particular space/time/frequency analysis is implemented for traveling-wave Vivaldi antennas, in which the phenomenon of EM energy transfer out of the conducting elements into the free space and higher-order scattering processes are revealed. The refined adjustment and optimization for the antennas are also proposed.