Every time UEFA holds a draw, I get more and more baffled that it can't be watched on television. While their rules against using the real names of stadiums if they're sponsored suggests that they might be about something other than being corporate shills, everything else they do suggests the opposite. That is, except for the fact that they don't sell the rights to their draws to TV stations or put ads on their online stream.
In any event, they show the draw for free on their website, which is awesome. Starting at 7 am ET, 11 am UK and 12 pm CET (daylight savings time means the U.S. is one hour closer to Europe than normal at the moment), you can catch a live stream of the Champions League draw at UEFA.com. There, you can see UEFA general secretary Gianni Infantino and his cast of whatever famous footballers he gets to join him draw balls out of bowls to determine who will meet in the Champions League quarterfinal.