Best practices or patterns for "Saved Search" and "Edit Saved Search"?

I have been tasked with redesigning our saved search function, as it has been deemed confusing (and I can't find another site that works like ours does currently). Are there any standard ways of handling both Saving a search and then allowing people to edit and save changes to a search? I have checked out what Ebay does. Is that fairly standard?

Edited to include the ebay (UK) example: