No one-stop solutions. How about a two-stop solution?
Set up encrypted conference calls via VoIP using ZFone. Combine this with an on-line conference call service which uses Asterisk software.
• Participant requirements
-- Access to the Internet.
-- ZFone software on their computer (lap or desktop). It's FREE.
-- Optional, for added privacy:
--- A plug-in headset $3.99
--- Or, plug-in ear-buds $23.99
• Teleconferencing requirements
-- Schedule calls with an Asterisk-based provider, like Rondee. It's FREE. (others)
-- Major carriers offer secure 'web-meeting' services for a fee. (example)
Note: Conference providers have access unencrypted calls; CALEA.
Other options
• VoIP telephony - Just route all calls through a Virtual Private Network (VPN). Good for inter-company conference calls.
"Very occasionally, there is a half second of delay when you have a few VPN-based users on a conference call together, but that has a nice social side effect of stopping people from trying to interrupt each other." Posted by Bradley M. Kuhn on June 20, 2008.
• Polycom Encrypted Video Conference Calling (Point to Point)
As I learn of new solutions I will let you know.
Until then, I hope this helps.
Kevin