More 'importantly', [=it is more important that] the proposed law will have a harmful effect on funding for public schools.
Her research has contributed 'importantly' to our understanding of the disease.
He strutted to and fro 'importantly', ordering everybody around.
(..) - Oh, hey, Alan. How are you? - Good. - What you doing? - Oh, me? I'm moving into my new lab. More importantly, where have you been? I heard you missed your Monday lecture and both of your students complained. Oh! I took a quick vacation. Best thing I could've done. (..)2008 Journey to the Center of the Earth