I came accross the following error while remoting to a standalone computer:

WinRM cannot process the request.
The following error with error code 0x8009030e occurred while using Negotiate authentication:
A specified logon session does not exist. It may already have been terminated.

Because for all other computers I am using Kerberos authentication, I was not aware that the TrustedHosts parameter was not configured (because Kerberos doesn’t need it).

To fix this issue, configure the TrustedHosts parameter on the client computer:

Set-Item -Path WSMan:\localhost\Client\TrustedHosts -Value 'Computer1,Computer2'

Or less secure but works too:

Set-Item -Path WSMan:\localhost\Client\TrustedHosts -Value '*'