The ITER Electron Cyclotron Heating (ECH) system will produce a high-intensity beam of electromagnetic radiation for plasma heating. A total of 20 MW of power will be transferred from 170 GHz gyrotrons through multiple transmission lines. The transmission lines consist of evacuated, aluminum, circularly corrugated waveguides that will each transmit up to 1.5 MW for up to 3600 seconds. The waveguides, as well as mirror and polarizer components, will be actively water cooled in order to support the heat load from the long-pulse high-power radiation. Transmission lines will be as long as 200 meters, made up of individual lengths of 2 to 4 meter pieces that are joined by couplings. These couplings must retain high vacuum during operation, and maintain a very high degree of straightness between adjacent waveguide pieces. Analyses have been performed to examine various parameters of the design of these couplings, and confirm that stringent criteria are met during installation and operation. Further couplings are used to join the waveguide to other transmission line components, such as miter bends, expansion units, and switches. All of these are analyzed to confirm structural integrity during operation.