You could look into calling CredUIPromptForWindowsCredentials:
From MSDN:
The CredUIPromptForWindowsCredentials
function creates and displays a
configurable dialog box that allows
users to supply credential information
by using any credential provider
installed on the local computer.
But there is more to this than simply displaying the dialog and recieving / acting on input - you'll most likely be required to register an authentication provider on the system, among some other things I'm not entirely competent with explaining in any detail! Might give you a decent starting ground though.
UPDATE:
Oded compensated for my laziness and supplied the pinvoke.net link displaying definitions for this to be used in a managed environment:
CredUIPromptForWindowsCredentials PInvoke.NET Link