After much frustration with Google's Custom Search Engine, it seems that Google's CSE doesn't actually support the Opera web browser. Apparently, when Opera users try to set up the Google custom search engine, they fill in all forms, hit save, but nothing happens.
AdSensePro eventually weighs in on the desperate forum discussion and says that Opera is not a recommended browser:
Our engineers have investigated, and inform me that this is an issue with Opera. We do not support this browser, and recommend you use IE or Firefox 2.
Forum discussion continues at Google Groups.