Question: Appraising a Map’s Value?

From time to time I get a question from someone who wants to know how much a map they have is worth. I’ve been reluctant to post these questions individually because it could be construed as free advertising; also, the question and answer, being so specific, would be of limited value to other readers.

At the same time, it is a reasonable question. So let me phrase it in general terms: how should someone go about determining the monetary value of their maps?

I presume there are appraisers who specialize in antique maps. Are there also online resources for this sort of thing? Or, if you yourself know something about the subject, what sort of things make a map more or less valuable?