This article Describes how to show estimated delivery against individual shipping options so that your customers can have an informed idea of when they will be receiving their goods, the below screen shot shows the shipping options available for my order, the only option showing estimated delivery is the 'Priority Courier Delivery':
If I also want to show the estimated delivery on the 'Special Delivery Guaranteed 1pm' option, i need to go to my Courier Integration page which can be found at https://ship.citruslime.com, once logged in I then go to 'Setup Services & Rules' within here I click the 'Edit/Add Services' Button:
As below find the service you want to show the estimated delivery for and click on 'Edit', this will open the details for the service, you will then need to change the eCommerce Basket Name so that it contains the word Priority or the word Premium:
After adjusting the name as above I click update.
I can now go back and refresh the page on my website and see that the service in question now shows the estimated delivery as below: