IF YOU'RE GOING TO WORK with dragons, once in a while you're going to get burned. Emilia Clarke found this out not too long ago in London while on break from filming the culture-conquering HBO series Game of Thrones. On the show, Clarke plays Daenerys "Dany" Targaryen, an exiled royal trying to win back her place on the throne, and the steel-willed mother of a trio of fire-belching beasts. She's one of the toughest television matriarchs since Carmela Soprano, and it's a character (and a performance) that demands respect. But on this particular night, there was this one guy.

"It...