I'm trying to find a serif and san serif that will look nice with Bickham Script, maybe News Gothic and Garamond?
How about Hoefler Text (and Hoefler Titling)?
And maybe Knockout as a sans partner for Hoefler Text, H&FJ have an example on their website.
Those may look good, but are they suitably neoclassical (18th century)?
Hoefler Text is an oldstyle, and knockout is Victorian.
Caslon or better yet the definitive transitional face, Baskerville, would be the obvious choices for the serif face.
For the sans, something anachronistic such as Sebastian or Eureka Sans.
This is just theory, I haven't actually put the faces side by side to see waht they look like, it's just the principle of historical allusion, that faces from the same era may be good pals. Something about shared aesthetic concerns, according to Hudson.
I like the way you think, Nick. I am yet to pair them, but I would think that they would do fine.