we are using the google search appliance in our web app. It is used by several other parts of our organization but we are using it on a web app that uses https. So, we followed google's instructions to get all the google code via https so that users don't get the annoying "This page contains both secure and insecure items" popup. Most of the google code has behaved and come to us as https, but there is a part of it pulling from http://www.google.com/cse full URL =
that causes the insecure items warning to popup.
This popup occurs in the results page and the above URL is the only non-secure request I can find.
Update. It turns out we didn't follow a specific Google doc to make this happen, but instead a series of forum posts. Most recently we are trying to follow this one: http://www.google.com/support/forum/p/webelements/thread?tid=64ebdf5fd3839c2d&hl=en