You’re right: the person who did the asking does the paying. I’ve been taken to lunch by a number of women, and enjoyed it very much. If the male guest won’t take “no” for an answer, simply say, “Sorry Jim, this one’s on me. Next time, you can treat.” Be firm but kind, which, by the way, is a good business trait to display anyway.
To avoid tussling over the check, tell the maître d’ or waiter when you arrive to bring you the bill at meal’s end. Then, instead of putting the check on the table along with your cash or credit card, which gives your guest the chance to take over, hold onto the bill until you can hand it to the waiter.
Even better, arrange payment in advance by giving your credit card number when you make the reservation, and asking to charge the cost of the meal plus a 20 percent tip. That way, no check is brought to the table, and there’s no question of who pays.
Source: Post, Peter, "Etiquette at Work," Boston Globe
For counter service, if the host wants to pay they should make the offer clear and either go first with an invitation to follow or mention to the cashier that they will pay once it is their turn in line.