Handling of Session for a site running from more than 1 data center

If using a DB to store session(used by some app server, ex.. websphere), how would an enterprise class site that is housed in 2 different data centers(that are live/live) maintain the session between both data centers.

The problem as I see it is that since each data center has their own session database, if I was to flip the users to only access Data Center 1(by changing the DNS records for the site or some other Load balancing technique) then that would cause all previous Data Center 2 users to lose their session. What would be some pure hardware based solutions to this that are being used now? That way the applications supporting the web site can be abstracted from this.

As I see now, a solution is to possibly have the session databases in both centers some how replicate the data to each other. I just don't see the best way to even accomplish this you are not even guraunteed that the session ID's will be unique since it's 2 different Application Server tiers(again websphere). Not to mention if the 2 data centers are some distance apart this could be difficult to accomplish as well.