I maintain a fairly old and very large site, which contains extensive classic asp code. Currently I use an old version of Microsoft FrontPage to manage it, but would like to move to an editor which supports HTML5 and helps the process to modernize my code.

So far on my trial I like CoffeeCup HTML Editor, but I'm fighting with some areas where the preview is faulty - triggered by inline asp code which upsets CoffeeCup.

Any advice on whether this is the right tool for my application?

I never use ASP myself, so I don't know what to say to the preview failures. The HTML Editor supports html 4 and 5, css 2 and 3, php and xhtml1. My guess is, that you won't be able to use ASP, but not absolutely sure.

I would add that you would have to determine exactly what the asp does and whether it can be replaced.
I would think that with a few changes the editor will give you a site that is far superior.