I migrated a site from one server to another with a different hostname using this process:
1. copy files and adjust wp-config.php.
2. backup database
3. update the hostname in the database file
4. restore the database on the new server
I found that the Custom Sidebars plugin on the new server only had the original set of custom sidebars, not the ones that were created in the original site. I fixed this by recreating the custom sidebars and reassigning them to pages (as well as recreating the settings we had on the "Default Sidebars" tab). I checked and the values in the database seemed to be the same (sidebars_widgets and cs_sidebars in wp_options).
Is there something I need to do to get the Custom Sidebars settings to migrate to a new site? My production site is fine now but I use this process to update my test server.