Exchange Shell:

Assign Permission:
New-ManagementRoleAssignment -Role "Mailbox Import Export" -User "username"
Logout then log back in.

Run Export Request:
New-MailboxExportRequest -Mailbox username -ExcludeFolders “#Contacts#” -FilePath \\server\share\user.pst

Monitor Status:
Get-MailboxExportRequest | Get-MailboxExportRequestStatistics

Cleanup:
Get-MailboxExportRequest | Remove-MailboxExportRequest

Source: Stevieg

“#Contacts#” can be replaced for excluding other items:
Inbox
SentItems
DeletedItems
Calendar
Contacts
Drafts
Journal
Tasks
Notes
JunkEmail
CommunicationHistory
Voicemail
Fax
Conflicts
SyncIssues
LocalFailures
ServerFailures

Exchange Shell:

Assign Permission – requires logoff/logon before taking effect:
New-ManagementRoleAssignment -Role "Mailbox Import Export" - User "username"

Run Export Request:
New-MailboxExportRequest -Mailbox username -FilePath \\server\share\user.pst

Monitor Status:
Get-MailboxExportRequest | Get-MailboxExportRequestStatistics

Cleanup:
Get-MailboxExportRequest | Remove-MailboxExportRequest

Source: Stevieg

Exchange Shell:

search-mailbox -identity username -searchquery kind:contacts -deletecontent

Source: Technet

Register the snap-in:
Add-PSSnapin Microsoft.Exchange.Management.PowerShell.E2010

Source: Steve Hardie

Exchange Management Console

Organization Configuration > Hub Transport > Remote Domains

Delete “Windows SBS Company Web Domain – companyweb”.

This was used to send emails to sharepoint in SBS2008 but its redundant in SBS2011.

Exchange Shell:
New-MailboxRepairRequest -Mailbox user@domain.com -CorruptionType SearchFolder, AggregateCounts, ProvisionedFolder, FolderView

Event Viewer MSExchangeIS Mailbox Store to check progress:
10047 A mailbox-level repair request started
10048 The repair request successfully completed
10050 The mailbox repair request task skipped a mailbox
10059 A database-level repair request started
10062 Corruption was detected.

Source: technet

To enable sending as a distribution group in Exchange 2007 / Exchange 2010

EMS:
Add-ADPermission -Identity "group name" -User "user alias" -AccessRights extendedright -ExtendedRights Send-As

Outlook:
To test straight away, Download the offline address book (click Send/Receive tab, click Send/Receive groups and select Download Address Book).
Send test email from distribution list.

Increase MaxHeaderSize on Exchange 2007 and Exchange 2010

Emails with large headers/many recipients bounce to external senders with 4.4.7 Could not deliver the message in the time limit specified.

To check current configuration:
Get-ReceiveConnector | ft name, MaxHeaderSize

To set a new limit:
Set-ReceiveConnector “Windows SBS Internet Receive Servername” –MaxHeaderSize 128KB

Source – Exchange Inbox
Source – Technet