"Looking askance" refers to a skeptical, suspicious, or disapproving look. The opposite antonym of this phrase could be "looking approvingly," "looking positively," or "looking trustingly." Instead of showing doubt or suspicion, the antonyms signify that the person looks at something with confidence or support. Some other antonyms of "looking askance" could be "looking directly," "looking optimistically," or "looking encouragingly." All these words carry a positive connotation and can be used in contrast to the negative or doubtful expression conveyed by "looking askance.