"The first male that comes along typically sits in the same tree below a female. If another male approaches, he may fight for the right to mate. Once a dominant male is successful, he approaches the female and uses a spray of his urine on the female. Only a few drops touch the female, but the chemical reaction allows the female to fully enter estrus. Once this is accomplished high in the tree, the mating process takes place on the ground. When porcupines are mating, they tighten their skin and hold their quills flat, so as not to injure each other. Mating may occur repeatedly until the female loses interest and climbs back in to the tree."

TL;DR: Q: How do porcupines have sex? A: carefully :-)

I'm going out on a limb here, but I have a sneaking suspicion that the porcupine didn't actually start this. So much for BBC impartiality, etc. :-)

http://www.bbc.co.uk/news/world-us-canada-34716175