Atletico Madrid were handed a chance to avenge last season's Champions League final defeat by city rivals and record 10-times winners Real after the two sides were drawn together in the last eight on Friday.
Paris St Germain and Barcelona were paired together having met in the group stage, with the French side winning in Paris and the Catalans coming out on top in Spain.
Porto will face 2013 champions Bayern Munich and Juventus take on Monaco in the other ties.
Real Madrid won last year's final 4-1 after extra-time against their local rivals, but Atletico's superb recent record against their more illustrious neighbours will give them huge cause for optimism.
The teams have met six times in all competitions this season with Real Madrid yet to register a win, while last year's final was Real's only victory in the last eight derbies.
Carlo Ancelotti's side have drawn three and lost four of those eight games while the last Madrid derby ended in a 4-0 win for Atletico, their biggest victory against their rivals since 1987.
Real's recent form has also been less than impressive having ceded the advantage in La Liga to Barcelona and suffered a surprise wobble in the last 16 against Schalke 04 when they slumped to a 4-3 defeat at the Bernabeu to squeeze through 5-4 on aggregate.
"Atletico are a very competitive team," Real director Emilio Butragueno told Canal Plus.
"But we are Real Madrid, we are defending the title and we will try to perform well enough to get through the tie."
Porto's clash with Bayern is a repeat of the 1987 final when the Portuguese side came out on top 2-1 in Vienna.
Bayern will start as overwhelming favourites, however, against an inexperienced Porto side, with the Germans offering a potent reminder of their pedigree in a devastating 7-0 drubbing of Shakhtar Donetsk in the last 16.
"There are certainly more uncomfortable opponents," Bayern captain Philipp Lahm said.
"But they (Porto) have showed their class. We will try to get in our away match an even better result than in the last 16. We are Bayern and we know what we have achieved in the last few years."
Holders Sevilla face Zenit in Europa League quarters
Meanwhile, Zenit St Petersburg will have to overcome a terrible record against Spanish clubs after being drawn on Friday against Europa League holders Sevilla in the quarter-finals.
Zenit, UEFA Cup winners in 2008, have won only twice in 14 games against Spanish opponents and are without a victory in their last seven against La Liga opponents.
Fiorentina's reward for demolishing Serie A rivals AS Roma in the last 16 was a quarter-final against Dynamo Kiev, while Napoli play VfL Wolfsburg and Dnipro Dnipropetrovsk play Club Bruges, the only unbeaten side left in the competition.
The ties will take place on April 16 and 23 with Sevilla, Club Bruges, Kiev and Wolfsburg set to play the home legs first.
Sevilla, three-times winners of the competition, have eased into the last eight and made light work of La Liga rivals Villarreal in the last round, winning 5-2 over two legs.
"Zenit are one of the strongest sides in the draw," said Sevilla technical secretary Oscar Arias whose side beat Zenit in the last eight en route to their 2006 UEFA Cup title.
VfL Wolfsburg will fancy their chances against Italy's Napoli having dispatched Serie A Inter Milan comprehensively in the last round, 5-2 on aggregate.
Napoli, however, may prove cannier opposition under European specialist Rafa Benitez, who is seeking to become only the second man after Giovanni Trapattoni to win the trophy for a third time after victories with Valencia in 2004 and Chelsea in 2013.
