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.
(..) Today, we acknowledge... ...a really terrible loss. Cedric Diggory was, as you all know... ...exceptionally hard-working... ...infinitely fair-minded... ...and, most importantly... ...a fierce, fierce friend. Now, I think, therefore, you have the right to know exactly how he died. You see... (..)2005 Harry Potter and the Goblet of Fire