The phrase "curling one lip at" refers to a facial expression of disgust or contempt. Antonyms for this phrase would include expressions of delight, agreement or admiration. Delighting could be expressed through a smile, laughter or expressions of joy. Agreement can be shown through a nod or a positive acknowledgment. Admiration can be expressed through a nodding of the head or a look of awe. These antonyms offer a range of emotion that can be used in different situations, depending on the intention of the individual. By using different antonyms, a person can convey a range of emotions that can affect the outcome of an interaction.