After I migrated my hundreds of users, I had some that were refusing to quit using the old webmail address. We were retiring the URL and therefore we couldn't just stick it on the new OWA server. To fix this, I disabled ActiveSync (for phones), OWA, and MAPI (for Outlook).
The code is as follows:
Get-Mailbox -OrganizationalUnit "Some OU" -DomainController "Some DC" | Set-CASMailbox -OWAEnable:$false -ActiveSyncEnabled:$false -MAPIEnabled:$false
A few days after this change, a couple of the stragglers relunctantly started using the new OWA.... and liked it.