Openwave 6.2 is an XHTML device, and therefore you need to install Device Update2 (DU2) on the server to get support for xhtml devices. You can download DU2 from the link here
http://asp.net/mobile/deviceupdate.aspx?tabindex=6
As for Openwave 4.11, you should be able to view the site fine since it is a supported WML emulator. Can u describe exactly what issues you are seeing with this device. It may be that you may have to do some customization on the site for this device, though the site should still be functional.
Hope this helps.