I very rarely, if ever, encounter markdown inputs where markdown is a superset of HTML. Almost always script tags and various other sorts of active content are stripped at the very least.
If certain tags are being stripped, then you're probably in a position where arbitrary input isn't desirable.
If this is an input to a website, for example, the webmaster really doesn't desire everyone to be able to reinvent the blink tag, or be able to express everything in rainbow fonts.
In which case Markdown shines, for it's ability to express simple markup, that can be safely expressed.
However, as Markdown is supposed to be nothing more than a superset of HTML, you can simply reach for CSS. It won't always render the best if you're moving from Markdown to physical medium, but that's largely dependent on the engine.