I've been asked this a few times now, actually. I often get told that my characterization of Wriothesley and Neuvillette is very strong, and my answer is always "I certainly hope so." And I don't mean that to make myself sound better xD It's quite the opposite.

I can write characters like I do, because I genuinely am able to get into their head. Sit down, grab a tea, and pull up a document. Think about your character, I'll use Wriothesley for example. I find a scenario, and I ask myself.
1. How would he respond to this?
2. How would he feel about this?
3. Is this scenario something he would approve of?
As some basic questions.

Getting into their head is a bit trickier. Watch some videos. Watch their mannerisms in the game, read their voicelines, stories, and interactions with other characters. Feel the way they portray themselves on the screen. They should feel that same way in your writing (unless you're actively trying an AU or don't want canon-based material).

Wriothesley, for me, is easy to write. Why? Because I understand him on a scary level. His innermost thoughts and emotions are easy to read when you have experienced forms of trauma like that. It's something that is relatable. (Not the killing of his parents but the emotional aftermath).

We can see that he keeps things close to his heart. He's a proud, yet humble man that doesn't think he deserves the respect he has. He does appreciate it. Think to his voiceline. "You can call me Your Grace. That's what everyone calls me down here, and I kinda got used to it." He's not saying that he dislikes the title, he just "got used to it." Meaning that there's hesitation there. It's something he's not used to.

The biggest thing I can tell you, is do your research. Wrap yourself into the character. Pull up some research online. You'd be surprised how easily things will flow to you once you understand how humans react to certain situations. Look at psychology papers, and read up on studies that have been conducted.

Let your characters tell the story for you. You'll be surprised to see what they have to say. I've had Wriothesley grab me by the shoulders and shake me like: "Do you really think I'd do that? Come on Surii, you know me better than that. Let me show you."

Listen to them. Observe, and record the story they are trying to tell you.