In Shakespeare's Act Two, scene one, of The Taming of the Shrew, I can surmise that Katharina is enjoying her conversation with Petruchio in that they both participate in an extended verbal fencing match. Petruchio may be the first man to have been able to keep up with Katharina's insults and return them at the same time. The battle of wits continues for quite a time and Katharina does not dismiss Petruchio and leave. She may also respect him because when she slaps him, he does not fold in half and retreat. For example, when Hortensio returns from trying to teach Katharina the lute, and she has smashed him on the head with it, he is dazed and drained by the incident. However, Petruchio stands up to Katharina and in some ways, gets the upper hand: he calls her "Kate," and gets her father's consent that they marry.
Petruchio is quite an opponent, and I believe because he is not weak and does not back down, that she respects him. I think she is also entertained by his wit and enjoys their conversation.