<p>Is it possible to have transport security without authentication? I'm well aware of it's flaws but atm I can't install a certificate a the client side.
It seems I can set WSHttpBinding.SecurityMode to Transport and the ClientCredentialType to HttpClientCredentialType.None, but when I try to call the service I get this exception:</p>

<p>An error occurred while making the HTTP request to <a href="https://[MyService]" rel="nofollow noreferrer">https://[MyService]</a>. This could be due to the fact that the server certificate is not configured properly with HTTP.SYS in the HTTPS case. This could also be caused by a mismatch of the security binding between the client and the server.</p>

<p>I don't think it's a mismatch of the security binding between the client and the server because I'm using a proxy generated by svcutil.</p>

<p>Why's it looking for a server certificate if I've set the ClientCredentialType to None?</p>

What you have set up looks correct for what you want.
I think that the problem relates to the difference between the certificate needed to ensure transport level security (HTTPS) and any certificate needed for authentication.
To perform transport level security you need to configure a certificate for the IIS server to use for its encryption. This is in no way used to identify parties in the WCF communication, just to secure the communication. (the certificate used for this HTTPS transport is also used to identify the server but that isn't related to WCF identity)
Here is a link to a
blog post
explaining how to set up a certificate in IIS for this purpose. Not necessarily the best google has to offer, just the first I found that covered all the important points. MSDN should cover this in detail too.