Is there any way to "restore" a .pst (Outlook Personal Folder) or .ost (Offline Folder file)?

I have had success with two different methods:

Method A

1. Save your pst/ost files (copy to a safe place via windows explorer)
2. Re-install Outlook and set up the account, but prevent it from downloading anything.
3. Note the location of the pst/ost files for the new Outlook installation
4. Close Outlook
5. Via explorer, replace the new installation's pst/ost files with your saved ones
6. Restart Outlook

Method B: Also I have used the previously mentioned Outlook import feature:

• File > Import and Export > Import from another program or file > Personal Folder File (.pst) > locate PST/OST > Import

As for the difference between PST and OST files:

• OST files cache the files from the exchange server; they are "copies"
• PST files exist only on one computer; they are not stored on the Exchange server

Sure... there are 2 ways:

• just put your .pst file at the default location BEFORE you start outlook for the first time (usually that's somewhere under your user folder/appdata/microsoft/outlook/...)

• or you can open outlook first, and then open your .pst file and then mark it as the default pst file and then remove the original one.

Edit
Concerning the .ost files: have you tried the same? I think you will have to configure outlook first (the IMAP account settings) but don't download the headers, then shut down outlook en copy your old .ost and .pst files over, and then restart outlook... not sure if that will work though...

Maybe this can be interesting as well: Repair a .pst or .ost file in Outlook