How do I enable both PowerShell Remoting and SPN for SQL Server Reporting?
I believe we have found the solution. To avoid Reporting Services and WinRM fighting over the HTTP SPN, you can set a port-specific SPN for the WinRM like this:  

setspn -S HTTP/&lt;Machine&gt;:&lt;port&gt; &lt;Machine&gt;  

It's a good idea to create SPNs for both short machine name and the FQDN.
The default port is 5985 for HTTP and 5986 for HTTPS, but I believe it can be set up to use different ports.  

When using WinRM, I just set up a session like this:  

$CimSessionOption = New-CimSessionOption -EncodePortInServicePrincipalName
$CimSession = New-CimSession -Name ServiceSession -SessionOption $CimSessionOption -ComputerName &lt;Machine&gt;
Get-CimInstance Win32_Service -CimSession $CimSession