Vfrdtyky

Since professor has masculine gender, one may think that the phrase should be professor emeritus, regardless of the gender of the person referred to. Is the use of emerita simply a case of grammatical ignorance?

In theory, the feminine of professor would be profestrix. However, this is a rather awkward formation, and isn't attested classically—the use of -trix on a dental-stem noun is incredibly rare in any period.

So most often, in my experience at least, the word professor is used for both the masculine and the feminine. If the professor is female, the noun is feminine, and thus takes a first-declension adjective like emerita. (For a Classical precedent, see gender-neutral third-declension nouns like homo and canis.)

To supplement the answer by Draconis, professor is what's called a common gender noun, at least in modern usage.
This means that the grammatical gender is not fixed, but depends on the semantic gender.
When referring to a male professor, professor is masculine, and feminine when referring to female.
I would consider it impolite in today's world to use professor as purely masculine word for professors of all genders.

The form professor emerita is correct.
While there is the feminine option profestrix emerita, this form is not really used.
The word profestrix is the Latin equivalent of the French professeure, but appears to be far less common.

Feminine forms such as doctrix and lectrix have been used and are in no way inappropriate for female academicians.
However, it appears to be more common to use the (seemingly) masculine words doctor, lector, and professor instead.

We normally distinguish between nouns of “common gender”, which can be used either as masculine or as feminine depending on the sex of the person or animal in question, and “epicene nouns", which have a fixed gender, but can refer to creatures of either sex. If “professor” is treated as epicene, then one would have to say “professor emeritus” for a person of either sex, at least in (Neo-)Latin.

In English there are no gendered forms for adjectives, so there is no reason not to say “emeritus professor” in reference to a woman in an English context.

In Germany there has been a heated debate over whether a female professor should be styled “Professor” or “Professorin”. In lecture lists of German universities you now normally find just “Prof.” - one way to dodge the question.