Should I use "authoress" for a feminine author?

Solution 1:

The term exists but it's considered "old-fashioned, sexist and patronising", as it says in my dictionary (NOAD):

-ess: suffix. Forming nouns denoting female gender.

• ORIGIN from French -esse, via late Latin from Greek -issa.
• USAGE The suffix -ess has been used since the Middle Ages to form nouns denoting female persons, using a neutral or a male form as the base. [...] In the late 20th century, as the role of women in society changed, some of these feminine forms became problematic and are now regarded as old-fashioned, sexist, and patronizing (e.g., poetess, authoress, editress). The ‘male’ form is increasingly being used as the ‘neutral’ form, where the gender of the person concerned is simply unspecified.

If you want a further reference also the OALD says the same thing.

Solution 2:

I'd say both are acceptable, though female author is probably more common. Authoress is now a bit old fashioned, I believe; it evokes a hint of romance and high literature to me, often in an ironic sense. In most cases, there is no need to express the sex of an author outside the use of pronouns (U.G. Liness uses this technique in her latest novel...): most people would simply use author for either sex.

I think gender is a bit more modern than sex, but, again, both are fine and quite common. In grammar, however, it is now nearly always gender.