Respectful alternative to "Madam"

To some extent it also depends upon the context. @Bill provides helpful examples pertaining to royalty.

You can also use Miss, Ms, Mrs. suffixed by first or last name depending upon her position relative to the speaker.

This link may help.

There's dame, ma'am, lady, or noblewoman. Unfortunately, most of these are reserved titles for royalty. The one I find the most commonly used is ma'am (which is short for madam), although this too is a term used in Britain to address the queen or a royal princess according to Dictionary.com.