Can’t send a Calendar sharing message

When you think you’ve covered the basics. This is one of those cases where a reader was part way through implementing Federated Free/Busy and Calendar Sharing between Exchange On-Premises and Live@EDU using the instructions in my guide, and when trying to share a calendar from an on-premises mailbox to a Live@EDU mailbox:

Hi Steve
Sorry - I'm stuck with this. Do you mind me bothering you some more?
I've set it all up, and sent my colleague (who has a 2010 mailbox) a calendar sharing offer and request from my admin@live.contoso.edu mailbox.
I've set his external email address on Live to in1150@exch.contoso.edu.
The invitation is delivered fine. If he opens the calendar of admin@live.contoso.edu from the message, he can see it, and it gets updated dynamically. However, when he tries to share his calendar with admin@live.contoso.edu (using the request in the message), he gets an error message:

This is very odd, because sharing is definitely set up with our domain…

That error again, for the benefit of anyone else experiencing this – “Your organization is not set up for secure sharing with this recipient”.

The first thing we did was check the basics for sharing were setup correctly which they were, but on further inspection and investigation into the Exchange On-Premises environment, the solution was pretty simple. For sharing to work you need to set the ExternalURL for the Exchange Web Services (EWS) virtual directory.
To set the ExternalURL attribute on the EWS Virtual Directory, use the following command against each of the Client Access Servers providing the facility to Internet clients, replacing servername and mail.contoso.edu with appropriate values for your organization:

Set-WebServicesVirtualDirectory -Identity "servername\EWS (Default Web Site)" -ExternalUrl https://mail.contoso.edu/EWS/Exchange.asmx