Recently, I was asked for one my customers, which is an Office 365 tenant, to share its free/busy information of Exchange Online with one of its partners ( another Office 365 tenant).
I looked for information about how to accomplish this, and my findings were out of the budget (some guys suggested to create an hybrid deployment on one of the sites). I even asked the question in the Office 365 community and the first answer was that it wasn't possible. The same MS representative replied days later with the solution: create organization relationships (aka Federated Delegation).
Long story short, in order for two Office 365 tenants to share free/busy information, you need to use Power Shell to connect to Exchange Online and then run the following command:
Get-FederationInformation -DomainName <the other cloud-based organization> | New-OrganizationRelationship -Name <the other tenant domain> -FreeBusyAccessEnabled $true -FreeBusyAccessLevel LimitedDetails
The full sequence of commands is:
Remember to do this command in both tenants if you want to have a both sides relationship.
Next, instruct your users to share their calendars with users in the other tenancy:
Finally, users on the other tenancy will be able to see free/busy information when creating a meeting request: