If the floor joists run continuously from the main house to the attached unit, any 'clamping' would probably just change the frequency of the impact sound transmission; if they don't run continuously, bracing the joists in both sides to the nearest joist is recommended . A floating floor above the existing floor or a new engineered subfloor, such as Quietwood, would likely be effective, but you would lose the antique flooring.

See also: www.nrc-cnrc.gc.ca/obj/irc/doc/pubs/nrcc49468/nrcc49468.pdf "Guide for Flanking Sound Transmission in Wood Framed Construction"

(GW does not accept pdf links)

Ah, better yet, a Guide from the same authors: www.nrc-cnrc.gc.ca/obj/irc/doc/pubs/rr/rr193/rr193.pdf

Thanks very much, Worthy - I'll check these out.

If the joists are continuous from one unit to the other over a crawl space you might build a new supporting wall under the dividing wall that would absorb some of the structure borne sound and also create a barrier for air borne sound in the crawl space.

You can also install solid blocking under the party wall between the joists to break up the sound path.

Stopping airborne sound is not usually all that hard.

Stopping conducted sound (like footsteps on a floor) is significantly harder.

You may also want to look into installing MLV (Mass Loaded Vinyl) under the joists. The MLV should absorb much of the vibration travelling through the joists. As brickeyee stated, conducted noise, or impact noise, is tough to deal with.

Another solution would be to put a sound deadening underlayment atop the new floor, like Impact Barrier.

Here is a link that might be useful: Impact Barrier