The world number one got the better of her Chinese opponent in the final of the Miami Masters on Saturday and was seen to be very friendly with her during the trophy presentation.
"I said I was happy for her, and us, and how we're doing," Williams told reporters. "We're playing great tennis and we're No.1 and No.2, and we're both the same age. For me it was just an honour to be there with her.
"We're living the same life, and at this stage, to be on top, I don't think it's been done before, and I think it's really awesome. I definitely feel like she deserved praise - especially winning the Australian [Open] was great. I just feel a connection with her that I just love.
"I just really like her as a person and as a player, and I have so much respect for her. It's great when we get to play each other, because she always gives it her all. From the first time I ever played against her until today it's always been the same."
Williams won the final 7-5 6-1.