In a previous blog I explained how to enable MFA for Admin accounts. This is a great security solution, but unfortunately it breaks Remote PowerShell for Exchange Online.
When you try to connect to Exchange Online using the following commands:

$Cred= Get-Credential
$Session= New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/PowerShell-LiveID -Credential $Cred -Authentication Basic -AllowRedirection

It fails with the following error message:

New-PSSession : [outlook.office365.com] Connecting to remote server outlook.office365.com failed with the following error message : Access is denied. For more information, see the about_Remote_Troubleshooting Help topic.
At line:1 char:11
+ $Session= New-PSSession -ConfigurationName Microsoft.Exchange -Connec …
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ CategoryInfo : OpenError: (System.Manageme….RemoteRunspace:RemoteRunspace) [New-PSSession], PSRemotingTransportException
+ FullyQualifiedErrorId : AccessDenied,PSSessionOpenFailed

As shown in the following screenshot:

To overcome this issue, Microsoft has a special Exchange Online PowerShell module that supports Multi Factor Authentication. You can download this from the Exchange Admin Center in Exchange Online by selecting hybrid in the navigation pane as shown in the following screenshot:

Click Configure followed by Open to download and start the setup application. Click Install to continue. The Exchange Online PowerShell module will be automatically installed in seconds and when finished it will automatically open a PowerShell window as shown in the following screenshot:

You can now use the Get-EXOPSSession -UserPrincipalName admin@tenant.onmicrosoft.com command to logon to Remote PowerShell. A separate windows will be opened requesting your tenant credentials, followed by the MFA option you’ve configured.

If all is entered correctly the Remote PowerShell for Exchange Online is opened with MFA enabled.