Get-OrphanedMailbox.ps1

function Get-OrphanedMailbox {
    $ExSplat = @{
        ConfigurationName = 'Microsoft.Exchange'
        ConnectionUri     = 'http://exchange.example.com/powershell'
        Authentication    = 'Kerberos'
    }
    $ExSession = New-PSSession @ExSplat

    Import-PSSession -Session $ExSession *>$null

    $SharedMailboxes = Get-Mailbox -RecipientTypeDetails SharedMailbox

    foreach ($SharedMailbox in $SharedMailboxes) {
        $Permissions = $SharedMailbox | Get-MailboxPermission | Where-Object {
            $_.IsInherited -eq $false -and $_.User -like 'EXMAPLE\*' -and $_.User -ne 'EXAMPLE\serviceaccount'
        }

        if ($null -eq $Permissions) {
            $CalendarIdentitiy = '{0}:\Calendar' -f $SharedMailbox.PrimarySmtpAddress
            $CalendarPermissions = Get-MailboxFolderPermission -Identity $CalendarIdentitiy | Where-Object {
                $_.User -notin @('Default', 'Anonymous') -and $_.User -like 'EXAMPLE\*'
            }

            if ($null -eq $CalendarPermissions) {
                [PSCustomObject]@{
                    Mailbox = $SharedMailbox.Name
                    SMTPAddress = $SharedMailbox.PrimarySmtpAddress
                }
            }
        }
    }
}