When Cate has a panic attack during the Godzilla evacuation drill, Emiko is the person to calm her down by holding her and telling her it will be okay. An impressive level of sympathy and compassion to display to someone who is the daughter of the man who apparently cheated on you (And who, although somewhat understandably, had previously been very rude to you and your son).
Making it even more heartwarming (or a tearjerker depending on how you see it) is that she is giving Cate what she should have gotten from her father in the aftermath of her experience on G-Day. Comfort, a hug, and reassurance that someone is there for her.
"The Way Out"
Cate and Kentaro shared a moment when their father used to act serious, then suddenly break into song from his favorite commercial. This is one of the few times they act like siblings over a fond childhood memory.
The fact that Kentaro’s starts singing just to cheer Cate up after noticing her PTSD flaring up. Compare this to how he was seemingly apathetic to her when they had the safety drill in Tokyo.
May helping Cate through her anxiety attack.
"Terrifying Miracles"
When Godzilla reveals himself to be still alive, while Shaw looks on in disbelief, the others react in awe and happiness, especially Keiko who thought the Monster King had been killed.
In the present, Keiko's granddaughter Cate has a similar response when she sees Godzilla once again. Ever since San Francisco, Cate has had nothing but fear of Godzilla to the point of suffering nightmares about him. However, one look in Godzilla's eyes and she sees something more than a monster, recognizing him as an great ruler who just wants his kingdom to continue.
