Respectfully describes words and actions that show honor and worth. When people behave respectfully toward one another, they are polite and take the other people's feelings into consideration.
The adverb respectfully describes the way you treat or interact with someone you hold in high regard, admire, or perhaps simply have been told to treat with politeness. You can also behave respectfully by upholding certain traditions, like singing your school's alma mater and standing for the national anthem at sporting events. Don't confuse it with respectively, or in the order given.