This is how I just got Outlook 2007 connecting to Exchange 2007 where the Exchange server is at a remote location.
Firstly, I have already made sure that HTTPS is allowed through the firewall on the Ex server. There is also a proper SSL certificate which as well as the main name, also has autodiscover.ExternalFQDN assigned to it.
From within Outlook here are the bits which made it work;
If the local name of the Exchange server is different to the external FQDN use the internal one as the server name. Input the windows user name for the mailbox name.
Do not click "check name" instead click "More Settings..."
Click the "Security" tab and ensure the following is set
1) The box to encrypt data between Outlook and Exchange is checked
2) Set logon network security to NTLM password authentication
Click the connection tab and then check the box to enable your connection to Exchange to use HTTP and click the "Exchange Proxy Settings..." button
Now, add the base URL in the first box, e.g. mail.contoso.com
Check the box for SSL only and also check the box beneath that, "Only connect to Proxy servers..."
Type msstd:Base URL e.g. msstd:mail.contoso.com
I check both the boxes below for connecting using HTTP first (a personal preference)
On the dropdown for "Proxy authentication settings" make sure that "NTLM Authentication is selected
Click "OK" twice to get back to the main e-mail account settings and click "Next" then "Finish"
Finally click "Close"
Now, when you run Outlook for this account, you should get a pop-up window which prompts you for a user name and password.
You should after entering the windows account name and the associated password, get through to the mailbox as if your PC was on the same network as the Exchange server.
One final thing, if the FQDN of your server is not Internet visible, e.g. it is mail.contoso.local
You may find that it will help to make things work if you alter your windows HOSTS file (c:\windows\system32\drivers\etc)
And add the following two lines, using the above server FQDN as the example;
External IP address mail.contoso.local
External IP address mail
That last bit may not strictly be necessary, but it will certainly make things a bit smoother.