It's small, but Kathryn manages to briefly escape from the Lonely Mountain by drugging Smaug with strong sedatives she had forgotten in her pocket.
Simply managing to stay alive for nearly a full year as the prisoner of a wrathful, possessive and homicidal dragon is impressive in itself.
When Kathryn ends up in a possibly lethal vision involving Sauron and the War of the Last Alliance, Smaug enters the vision and helps her to get out of it.
As foolish as the Knight of Gondor was to try and vanquish Smaug with just the Eluvienel Bow as his aid, points for trying to free the land of the dragon.
Heart of Ashes
On Queen Lalemwen's orders, Smaug is taken to the dungeons. Kathryn is in turn taken to her chambers immediately afterwards, and surprise, he has already escaped and waiting for her there.
Kathryn: What are you doing here?! You were taken — Smaug: Do not finish that sentence for it will only insult me that you believe I would even allow the notion of a pack of humans to keep me prisoner.
Lord Beronor: Perhaps the general is tired. His mind is fevered from his wounds. Like us all, he is ageing and simply does not want to admit that he lost his battle against the dragon due to his lack of sound judgement due to age — General Victis: Bastard! [unsheathes his sword] I may be old and tired, aye. But I had PERFECT judgement when I was out there with my men! It was not my judgement that made the arrows bounce off of the brute's scales! It was not my old age that gave that creature such a deadly ferocity that it tore my men apart with little effort! If you believe that our army is sufficient to take it down Beronor, then you won't mind when I volunteer you to be at the front line leading the men when the thing next comes!
At the end of that same scene, Queen Lalemwen decides to ask Erebor's dwarves to create any Black Arrows they can for whatever price they ask. Lords Beronor and Gregorse try to protest against asking help from people they planned to "discreetly" conquer. The gentle, pregnant and recently widowed Queen puts a stop to their nonsense in a way that makes the watching Quithyra proud to serve Lalemwen.
Lord Beronor: Your Majesty! We cannot go to others and beg for help! The words of Dorwinion have always been 'Strong and sure'. Queen Lalemwen: I do not give a damn about words when my people are in danger! If that dragon returns, I want us to live long enough to say that we swallowed our pride to survive so that we might have any pride with which to speak of. Lord Beronor: Your Majesty, please listen to us when we say — Queen Lalemwen: [rises up to glare at the Lords] I am the Queen. You. Listen. ToMe!
Gandalf faces Smaug in the 21st chapter, holding his own well against the dragon. Smaug gives a look that indicates him to consider the wizard a Worthy Opponent.
Heart of the Inferno
In the 7th chapter, Smaug faces Moria's Balrog in a vicious fight. Smaug has to use his brain as much as his brawn. See here for the author's drawing.
While Smaug's facing the Balrog, Kathryn tries to resuscitate Gandalf by transferring Raw Magic into him. When the Balrog appears over them, Gandalf temporarily wakes up to charge his sword with a thunderbolt and stab the Balrog's chest, after which Smaug finishes the creature off.