Squiring means accompanying and attending to someone, especially a woman, as an escort or a gentleman.
Squiring can have a polite and formal feeling. It can show care and respect for the person being accompanied.
Examples:
He is squiring the lady to the ball.
The gentleman is squiring the lady to the theater.
She is squiring her to the party.
The man is squiring the woman to the restaurant.
He enjoys squiring her around town.
The gentleman is very good at squiring the lady.