Just Smile and Nod

You've run into someone who's insane. Or really insane. Or perhaps just far more intelligent than you. If nothing else, you're not going to listen because you can't or won't understand what's happening. But you can't stop them, either for reasons of etiquette and decorum, or simply because you can't get a word in edgewise.

If this is the case, all you can do is smile, nod, and wait for the other person to finish.

Stock Phrase. Related to polite lie, compare Stepford Smiler.

Anime and Manga
"Dimitri: That move takes me back to our duel against Seto Kaiba at Battle City. Those were some good times, weren't they old friend? Syrus Truesdale: Battle City? This guy's gone batty! Chumley Huffington: Just smile and nod Sy, smile and nod."
 * Yu-Gi-Oh! GX. Dimitri is convinced he's Yugi Muto.

Film

 * Wizards of Waverly Place. Alex can't understand the locals, but uses a spell to create a literal caption floating in the air that translates for her. The locals talk about how she's a strange girl and maybe if they just smile and nod she'll go away.
 * There's a movie called Just Smile And Nod.
 * Played very sadly in Chaplin: Charlie has just gotten news that died several years previously, and reels from the news, trying not to break down in tears. Moments later, his train pulls into the station and a huge crowd of fans is waiting on the platform. A friend asks "What do we do, Charlie?" and he replies simply "Smile," referring to the famous song to which he wrote the music. He then gets off the train and greets them all as if nothing's wrong.

Literature

 * Discworld: This is the Arch-chancellor's stock reaction when Ponder Stibbons tries to explain anything to him. At least, when he's not confused by the metaphors.
 * Also in Going Postal, Moist is a con man, and so demonstrates how good he is at this when some people who run the clacks go into technicals.

Live Action TV
"Will: Now remember: agree with everything I say and disagree with everything they say. Carlton: Why don't I just smile and nod? Will: [beat] Even better."
 * Brought up in Doctor Who on how to respond to the Doctor explaining something that makes no sense to...anyone else. Specifically in "Blink", Martha notes you should just nod when he takes a breath.
 * Also brought up in The Fresh Prince of Bel-Air, when Will and Carlton are about to have a meeting with some record company executives:

"Servo (as Eulabelle): Just smile at the stupid white people..."
 * In Numb3rs, The FBI gang do this when Charlie explain some very complicated math theories.
 * Used as a joke in the Mystery Science Theater 3000 episode Horror of Party Beach, in reference to an Only Sane Man black maid:

"Nobleman: He thinks he was there. Play along."
 * In general, this is the reaction the bots give Mike whenever he begins a Sanity Slippage or a Thousand-Yard Stare.
 * In one episode of Sharpe the titular hero ends up at dinner with Mad King George (the third, to be precise), who starts telling the tale of one of Sharpe's earlier adventures to his guests. One of the other gentlemen present kindly explains the situation:

Video Games
"Veradux: Just shut up and nod, Sonny."
 * In the first Sonny game, when Sonny and Veradux meet up with the paladin who's trying to take down Baron Brixius, the paladin mistakes them for two members of the three-soldier team meant to back him up (Sonny and Veradux killed them on the way to the paladin's location).

Web Comics

 * This is a general reaction to Hannelore from Questionable Content as shown here.

Web Original

 * A facebook group.

Western Animation

 * The Penguins of Madagascar: One of Skipper's catchphrases. "Just smile and wave, boys," along with, "Cute and cuddly, boys, cute and cuddly." Also used in the first movie.