A novel scheme involving experimental analyses and diagnoses is presented for monitoring radio-frequency (RF) and high-speed circuits. A live electrooptic imaging (LEI) camera is used in the scheme and it provides real-time images of the phase evolution of the RF electric field. Besides, it is demonstrated that essential properties of RF wave propagation are easily grasped from visual images; examples of LEI movies and images from which such essential properties can be identified are presented. The subjects of the LEI observations, analyses, and diagnoses are planar RF circuits and a Gbps-class emitter-coupled-logic circuit. In addition, the results of analyses and diagnoses in the space domain are discussed.