As in "to speak forsoothly".
To speak in a period manner or style. Most SCAdians speak in a formalized type of modern English. Period English is very difficult to recognize.
In addition to the SCA usage of the term, we should perhaps keep in mind that the etymology of the word "forsooth" comes from the phrase "for truth". I take this to mean that we should speak honestly, letting no word of a lie or hint of dishonour cross our lips, an especially salient concept in a close-knit (read insular) and talkative (read gossipy) bunch of people like the SCA.
-- *Briana*