I was tired of leaving my soggy sponge on the counter with the water running everywhere.

My solution is the Sponge Tray

It is designed to hold a common sized sponge.

The tray is slanted towards the sink to promote water drainage.
The insert is removable so you can wash or replace it if needed.
(Tray Insert has a loose fit making it easy to remove)
A non slip material can be applied to the bottom of the Sponge Tray.
Though I didn't find it necessary.