I ran geany without sudo. I opened a file (jail.local) and modified it. Now I can't save it back to the original file. Is there a way to execute a [menu] command (e.g. File/Save) "as super-user"?
If your question is specific to Geany, the answer is No. Geany has no option to dynamically switch to the role of a privileged user. The only viable option is save the changes to another file (possibly with same name) using the Save As feature and then move the file back to original location using
sudo mv replacing the original file. That will do the job of saving.
But, if you're looking for any generic GUI application that will allow you to save as root without opening it first as root, there is Sublime Text 3.
Sublime Text has a feature which will ask you root password when you want to save edits made on system files, even if you originally started it as a normal user. You may consider it in place of geany from now on.