Put simply, just about every interaction between Ilya and Shirou either has or is one of these.
In Chapter 1: Shirou has just met Ilya, and has no idea of who she is, why she gave him a cryptic warning... nothing. Yet despite this - and an instinct screaming him that approaching her would be risking death - he reaches out to her. He puts on a big-brotherly expression, he offers to walk her home or lend her money for the bus service, he compliments the hair she inherited from her mother... and in the end, the part of Ilya that still yearns for affection wins over the ten years of cynicism drilled into her by the Einzberns.
In Chapter 6, he's out to get supplies for lunch (for Saber, among others), and runs into Ilya again. After some small talk, she asks - and then begs - him to give her a tour of the town just to spend time with her. Despite knowing he'll get in trouble if he delays getting back, he cannot resist the urge to make her happy. Following that...well:
The brief moment of shock at his acceptance, followed by the practical flood of joy into the girl's eyes as she latched onto his arm like a vice clamp, convinced Shirou that he had made the correct decision.
And then, he promises to meet her again tomorrow - and despite being sick from prana drain, he keeps his word.
In Chapter 14, Shirou meets Irisviel. She does not carry any emnity towards him or Kiritsugu for what Ilya went through the last ten years - she simply notes that he's been a miraculous influence on her little girl by giving her the affection she's been starved of, and asks him to do his best to save her. And though Shirou's unsure if he's dreaming or not, he accepts. Whether it's meant to be Ship Tease or not, it's beautiful to watch because either way, Iri seems to have accepted Shirou as her own.
Chapter 15: Despite her misgivings about Ilya, Saber jumps in front of Gilgamesh's attempt to skewer her and blocks the sword he fired from Gate of Babylon. Even better in that she also defended Berserker (who had leapt in front of Ilya first) from the attack, and declared a no-strings-attached Enemy Mine with them, against Gil. Ilya is left stunned, and actually realises that Being Good Sucks might not quite be true.
Saber: "Perhaps Shirou is influencing me oddly, to defend a potential foe so. Or perhaps I am still simply curious as to what you know about the oddities in this War. But this Archer is no ally of mine, Lady Einzbern, and I do owe you a debt of assistance. If you stand against him, then I stand with you."
Gilgamesh: "I'm sorry? Did the meat puppet forget that she does not have permission to speak?"
Ilya: "That's wrong! If... you love someone, then... then doing anything that makes them sad should make you sad. And making them happy makes you happy. You... if you have to force them to love you back then it's just... it isn't right. They should love you because they love you!"
Saber: <smiles warmly> "Well-spoken, Lady Einzbern. Perhaps choosing to fight by your side was a better decision than I had imagined."
In Chapter 20, Caster Alter offers to have sex with Sakura to restore Sakura's energy, but Sakura asks her not to be cold, as she's had enough of that from Shinji and others. They proceed to make love.
In Chapter 23, after Ilya lost Berserker, both Shirou and Saber pledge to act as her Servants as a form of penance (for Saber being forced to put down the possessed Servant. This causes her to blush in embarrassment, evidently moved and flattered by their (admittedly stupidin her mind) Honour Before Reason.
After being a massive Troll towards poor Shirou in Chapter 25, Ilya has a deeply vulnerable moment where she admits to him that although it might not mean nearly as much to him (which it does, but she doesn't know that), the kindness and warmth he's shown her from the start has made her genuinely happy for the first time since her parents left her life; she even remembers how compassionate and loving her father Kiritsugu was, the hate she had build up lifted like a fog thanks to his adopted son. Shirou melts and embraces her as he silently admits, in his mind, that having her in his life does make him happy.
Archer's realisation that Illya is actually throwing his plan out of whack... and resigning himself to not doing anything to counter that because he would never refuse her anything. Even lost in bitterness and cynicism, Shirou Emiya can't bring himself to not love her.
Caster's support of Sakura. Even while trying to corrupt her, she truly did care for her. Sakura admits she feels the same, but it doesn't stop her from killing Caster after becoming Dark Sakura to ease the pain and use her knowledge.
In Chapter 33, when Iliya reveals her days are numbered, she stated she did not want to reveal this to Shirou because she did not want him to treat her any differently and wanted to see him as happy for as long as possible. It's both heartbreaking and sweet.
Archer in his final moments when Shirou of all people actually cries for him. His final thoughts were about how he was glad that someone actually expressed sorrow for his passing. Something he did not get in life. Again, heartbreaking, but sweet.
After Shirou severs Sakura's connection to the Grail, he shields her from the backlash, holding her tight while saying "it'll be okay" to her.
In a dark way, Angra Mainyu summoning corrupted Servants from the character's past, even though they are trying to kill them. Gilgamesh is reunited with Enkidu and Iskander. Rider faces her younger self as well as her sisters Stheno and Euryale, who say they will fight together as a family. Saber faces Lancelot and Mordred.
To even the odds against Angra Mainyu, Illya and Sakura perform a mass summoning. Among the Servants who arrive are Medea Lily and Heracles as Archer. Though the two have no memory of their past summoning, Illya and Sakura are very happy to see them again.
Saber Lily is forced to kill Mordred again, but Mordred dies at peace because Saber had renamed her attack "Excalibur Mordred".