Outlook Web Access Certificate

You need a SAN or UC certificate.  I recommend GoDaddy  or www.domainsforexchange.net

http://blog.sembee.co.uk/archive/2008/05/30/78.aspx

One of the most important aspects of a successful Exchange messaging deployment is how you configure your SSL certificates for securing client communication to your Exchange infrastructure. This is because all communication between Outlook clients and the Autodiscover service  endpoint, in addition to communication between the Outlook client and Exchange services, occurs over an SSL channel. For this communication to occur without failing, you must have a valid SSL certificate installed. For a certificate to be considered valid, it must meet the following criteria:

- The client can follow the certificate chain up to the trusted root.
- The name matches the URL that the client is trying to communicate with.
- The certificate is current and has not expired.

Remember,  the cert request needs to be generated by Exchange using PowerShell.
 http://technet.microsoft.com/en-us/library/aa998327.aspx

When you get the response back from the CA, use the import-certificate command to process  and enable it for SMTP, IIS, etc.

http://technet.microsoft.com/en-us/library/bb124424.aspx

Very often we come across tasks where we have to create a new self-signed certificate or deal with related errors/warnings. Hope the following information serves you on those tasks:

Suppose we want to create a UCC self-signed certificate. We will require the following names:

#NETBIOS name of Exchange: EX-2k7 (example)
#Internal FQDN: EX-2k7.abc.local (example)
#External FQDN (Public name): webmail.abc.com (example) (use nslookup/ping to verify the external FQDN)
#Autodiscover name: autodiscover.abc.com (example)
#SubjectName: cn=webmail.abc.com (example)

In EMS, run the following command to generate the new self-signed certificate:

New-ExchangeCertificate -FriendlyName "SelfSigned Cert" -SubjectName "cn=webmail.abc.com" -DomainName EX-2k7,EX-k7.abc.local,webmail.abc.com,autodiscover.abc.com -PrivateKeyExportable $True

Next enable the certificate with Enable-ExchangeCertificate cmdlet. Enable atleast IIS and SMTP.

Enable-ExchangeCertificate -Thumbprint xxxxxxxxxxxxxxx -Services POP,IMAP,SMTP,IIS

Next verify certificate has been installed using EMS/IIS Manager or both. (Sometimes you may have to remove the certificate and then install/enable certificate again).

Some important points:

1. If you are creating a self-signed certificate, it is always better to create one that has all the subject alternative names specified above. This will prevent any certificate security warnings related to name mismatch. If you are creating single-name self-signed certificate, you would have to modify internal URIs of multiple virtual directories as explained in KB940726. The other benefit of multiple SANs is avoiding event 12014 and similar events.

2. Autodiscover for non-domain joined machines will work only after record is created in external DNS

3. You will have to install the certificate in the trusted root on client machines else you will receive a certificate warning. On Vista machines, you will have to run IE with elevated privileges to be able to install the certificate when you open OWA.

4. You can use group policy to install the certificate in trusted root (applicable only to domain joined machines). Copy to file the self-signed certificate (ideally in .p7b format) and then edit the default domain policy and import the certificate into "Computer Settings\Windows Settings\Security Settings\Public Key Policies\Trusted Root Certification Authorities". No user intervention is required once you do this. (Users would have to install the certificate themselves on non-domain joined machines).

5. SBS2008 Information: When you install SBS 2008, setup Internet Address wizard uses self-issued certificate by default. You will find it is "Issued to" "external FQDN" of the server and "Issued by" would be "Internal FQDN-CA" (SBS setup configures CA by default). When the wizard generates the self-signed certificate, it also generates a Certificate distribution package. The package (Install Certificate Package.zip) is located under one of the default shares named Public (C:\Users\Public). Another point to remember about SBS2008 is that the default certificate is single-name certificate and if you create a new one with multiple subject alternative names using the procedure above, you will receive a warning while enabling SMTP on the certificate. This warning can be ignored. You can verify availability of STARTTLS verb using Telnet.

If I have already generated my own certificate from our root certificate authority, can I just import that into Exchange and use that for synchronization between Exchange and Edge? Thanks.

yes you can use it for synchronization between edge and HUB for more information please refer my above comments

Good solution.