Using the Search control I am seeing content from pages flagged as "disabled" showing up in the search results.

Is this by design or is there something going awry in my site's search indexing?

What is the "right" way to prevent specific pages from having their content indexed for search?

Are those results also shown if logged in as a normal user?

Then it's most probably not by design. You could try completely removing the index from your database and forcing a rerun of the search index scheduler afterwards, to see if the disabled pages' content disappears.

If it doesn't: One workaround is to change the disabled pages' rights to not allow 'Everyone' to see it (just completely uncheck it). Search results will (normally) not show content the user doesn't have access to (just as it shouldn't show content of disabled pages either, but that part is apparently not working or, for some strange reason, by design).

Ash Prasad's method may do the trick as well.