Thanks for the reply - I don't know the server has active sync enabled. I'll have to ask the support guy.
A bit more digging shows that I have to connect via a proxy (the https address) and then specify the local domain name of the server. It's what used to be called rpc over http and I can't work out how to set the proxy in Touchdown.
Also, with Outlook on Windows, I have to import the certificate into the trusted CA store before it will work.
I have tried a range of settings and options to no avail. Ideally, I'd like a step by step to configure Touchdown for RPC over HTTP...