This is another nitpicky little set of steps that I always forget about and end up googling to get a solution to... so I figured I would finally write it down!
During the migration from SBS 2003 to SBS 2011, there is likely some point where you will have a number of users still on 2003, and a number of users on your new 2011 box. Wouldn't it be great if everyone could get their email, access OWA, etc etc regardless of their mailbox location, thus lessening the pressure to get everything done in one 'big bang' migration? Sure it would. Well, here's the steps (although admittedly not very detailed... just high level... individual steps can be googled for more info):
1) Follow the SBS2003 to SBS2011 migration guide from microsoft up to the point where you are ready to Migrate your mailboxes. At this point, Microsoft guides you through a disruptive cutover rather than a smooth migration, so some tweaks are needed.
2) Make sure your SSL is set up appropriately on both servers. There are a few details that are paramount in getting this right. For one, you need to have an SSL certificate on both servers. Each server must also have a unique SSL certificate, as they cannot both resolve to the same name... otherwise this won't work right. If you want to migrate your existing SSL cert from SBS2003 to SBS2011 that's fine... just make sure you remove it from 2003 at the end of it, and generate a new one (either paid, which is a waste, or using the SBS2003 "Connect to the Internet" wizard to generate a self-signed one).
3) Make sure your DNS zones are set up appropriately so that each server is resolvable by their SSL certificate name. If you followed the SBS2011 wizard, it should have done this for you automatically by setting up an authoritative zone for servername.domain.com in your internal DNS server. You should do the same for your legacy SBS2003 server and it's new SSL certificate name.
4) Go into the properties of the Exchange virtual directory under your Default Website in IIS on your SBS 2003 box and check the Directory Security tab. Hit the Edit button under Authentication and Access Control and ensure that "Windows Authentication" is checked, in addition to whatever else was already there. If it's not checked... check it! This allows the two exchange servers to pass authentication to eachother... without it, your users will get prompted for authentication twice.
5) On your SBS 2011 server, open up your Exchange 2010 management shell and enter the following command: SetVirtualDirectory "Servername\owa (Default Web Site)" -Exchange2003Url https://OldServerName.Domain.com/Exchange . That tells your Exchange 2010 server where to send OWA requests when the user's mailbox is on the 2003 server.
Done! Now, just reconfigure your firewall to send the HTTPS/SMTP/Whatever requests to your new exchange server instead of your old one, and you should be off to the races. Resume following the SBS2011 migration guide, ignoring any steps you already did!