Something that popped into my head from watching Yellowstone. I apologize if this sucks.
This can take place in either canon or Legends continuity, but I do draw more from Legends and consider it taking place after The Courtship of Princess Leia.
Corellia
Afternoon
"Never thought you'd come back here Mr. Solo," the cemetery caretaker said as he led Han through the cemetery.
"Well, never thought I'd come back here. But this was important," Han said.
"I hope so. This is one of the strangest requests I've ever gotten," the caretaker said as they stopped in front of a grave. "You sure about this Mr. Solo?"
"Yeah, I'm sure," Han said lowly, staring down at the grave solemnly.
In the old days, they buried their dead in the ground, Han knew. The bodies would decay until they were skeletons. Now, they locked the dead in caskets that stayed above ground and were designed to slow the process. The body would still decay, but it would take a lot longer.
All this ran through Han's mind as the caretaker opened the top half off a casket. The caretaker stepped back and Han walked over until he could see directly into the casket. Han looked down, seeing a woman with deathly pale, slightly decaying skin. She must have looked beautiful when she was alive, Han noted. It was silent for a moment before Han spoke.
"Hey Momma," Han said, his voice suddenly thick with emotion that surprised. "Sorry it's been a few years since I've been here. I got caught up in a few messes."
Han tried to swallow the lump in his throat. He didn't know why this was so hard. He had never even known his mother. Jaina Solo was just a name to him. But he'd always held onto the name, a part of his past that he felt some odd connection to.
"I'm getting married," Han said after managing to gain control over himself. "Her name's Leia. She's literally a Princess, or I guess she used to be. She's…amazing. I don't know what I did to deserve her, but I thank the Force or whatever cosmic powers are out there than she loves me.
"Wedding's in a few days. Everything's ready… except for one thing," Han said with a shaky breathe. "I need a ring for Leia. And I could probably just go into whatever shop on Construct and buy one. But she deserves more than that Kriff.
"Sorry," Han said as he caught himself. "I'm not sure if you would have liked it if I didn't swear or not, but I'll try not to. Anyway, Leia's given me so much. She made me a better man, she gave me a cause to fight for, she changed my life. I don't have anything to give her in return; I have nothing from my past of value. But I want her to have your ring Momma. I hope that's okay. I just…I want to give her something that shows she's not giving anything up. That I'm worth something. She may not think I'm not worth anything, but I want something to show that."
It was silent then, so Han took a deep breath. Getting on his knees, Han reached into the casket, taking his mother's cold hand. Then, slowly, he took the ring and carefully pulled it off.
"Thank you Momma," Han said lowly, gently placing the hand back inside.
Han then slowly closed the casket before standing up. Looking down at the ring, Han examined it. It was a simple gold band with a gem that Han recognized from the shots in the higher class parts of Corellia, although Han couldn't name what it was.
It was beautiful, yet fierce. Just like Leia. It was perfect.
Han taking his dead mother's ring off her corpse might seem morbid, but in his own Han Solo way, it's a testament to how much he loves Leia.
If Han seems out of character, well, I imagine that Han would allow himself to actually be vulnerable during this visit, so he'd be more open than he normally is.