Without a doubt, the Crowning Moment of Heartwarming in the show (and possibly the franchise) is Episode 41 "Teacher's Memories". After twenty-five years, Takeshi Yamato's students are reunited with their teacher one last time before their school is demolished. It's even more heartwarming when you find out the actors playing the grown-up students are the original kids from Ultraman 80, making it a truer reunion than it possibly could be.
A series-wide example — the friendship amongst the crew of GUYS is simply a pleasure to watch. While they do occasionally bug each other a little, they're extremely supportive of and deeply care about each other, always enjoying the times they share together and trying to help whoever's the most troubled of the group at the moment. They really are the truest of True Companions.
Seiji Hokuto reuniting with Yuko Minami in Episode 44 "Ace's Wish".
GUYS' barbecue party for Kako in Episode 36 "Mirai's Younger Sister" to make the alien feel welcome amongst them on Earth.
Episode 23 "The Ocean Waves of Time" has Torii's words of encouragement (telling her that in death, her loved ones will still be within her heart) to the young Marina, who can't stop grieving over her late and beloved grandfather.
The farewell scene between Mirai and his friends at the very end of the final episode, which borders on Tear Jerker.
In the credits of Ultraman Mebius & Ultra Brothers, footage of a Tsuburaya-held party for Ultraman's 40th anniversary is shown, featuring actors from the Showa series as guests honornote including Susumu Kurobe, Hiroko Sakurai,Kohji Moritsugu, Yuriko Hishimi,Jiro Dan,Keiji Takamine, and Mitsuko Hoshi. Near the end, the actors are presented with bouquets, some by Shunji Igarashi (Mirai's actor). Among the guests...all the Ultramen up to 2006. The Ultras each get a bouquet as well and the actors and silver heroes gather for a photo, but not before a montage with a clip of every Ultraman. A Heartwarming Moment for the warm feelings it gives for fans, but also doubles as an Awesome Moment for the amount of celebration filled into the footage.
Fanmade Example: This comic in which GUYS decides to get something for a homesick Mirai. It just captures the essence of GUYS so well.