gksudo with cool GNOME Shell integration
Solution 1:
That cool window in GNOME Shell is only displayed for applications that use PolicyKit. For example, to trigger this window for Synaptic, run this in a terminal:
pkexec synaptic
You can't use pkexec for all applications but only for those that have a pkexec policy file under /usr/share/polkit-1/actions/.
Solution 2:
For this you can use the command gksu-polkit. It largely behaves the same as gksudo, but taps into the policykit framework. To use it install the package 'gksu-polkit'.