When Kathryn ends up in a lethal vision involving Sauron and the War of the Last Alliance, Smaug enters the vision to help her out of it. When she thinks him to be a part of the vision and refuses to listen to him, he's forced to swallow his pride and ask her to trust him, promising not to let Sauron have her. He then instructs her to imagine them in somewhere safe and she imagines them inside the Lonely Mountain, much to his astonishment. After the vision's ended, he allows the grateful Kathryn to fall asleep in his coils, and he realizes he doesn't want to lose her.
Heart of Ashes
Heart of the Inferno
The end of the 9th chapter: Kathryn has given birth to her twins Kolstros and Vervenia, having survived the hard labour thanks to the recently resuscitated Gandalf the White. Smaug, having returned from fighting the Orcs of Dol Guldur and sensed Kathryn's near-death experience through their bond, is overjoyed by her survival and their twins' birth just as much as she and Gandalf are.