Is there a word for "to make humble" with a positive connotation?

I think the verb humble is at least more neutral than humiliate, although the connotation might not be specifically positive.

Some examples via COCA from various sources:

That's the sign that little Melipona, messenger of the gods, has been trying to deliver all along. The missive is so literal, I can't help but feel humbled - and connected. The message is simple and sweet.

It's so amazing to have my name on a list with these other women. I feel very humbled by it. I just feel honored.

I don't think these examples carry the negative connotation that humiliate does.

Perhaps a slight variation on humiliate -

"Having children of my own gave me a new humility."

While they both come from the same Latin roots, humiliate now means

to hurt the pride or dignity of by causing to be or seem foolish or contemptible; mortify

but humility means

the state or quality of being humble; absence of pride or self-assertion

This is not a negative connotation, but neutral to positive.

If you are going for a meaning along the lines of being less accepting, less harsh or strident, or more mature or developed, you could consider mellowed, matured, or softened. These are all positive attributes.

"Having children of my own softened me."