To answer the question - found an embassy with the Civ and you will see their capital.
As to the intent - why do you need to see their capital to establish a trade route? Generally, if you see a city that they control and it has roads going in/out, it is usually connected to their entire empire. Depends on how early the game is as to the "usually". But the AI connects its cities fairly quick if it has the means. So connecting to any one of their cities usually completes the trade route. If the civ lines are really messed up, there might be other problems though - the Civ's city might be cut off from its empire by another hostile civ, etc.
I can't think of a time where I have connected to a Civ's city and not completed a trade route - meaning I was only connected to the one city. Not sure how that would work, but it might just be a theoretical problem. Maybe someone else has encountered this.