I feel pretty stupid right now. I've set up two email accounts in Evolution, nothing special: IMAP and SMTP.
But I can't find anywhere to enter the password. I thought maybe I'd be asked for it after the first account retrieval, but that didn't happen. Later I read that Gnome Keychain might be involved. But nothing at all is happening.
Next when you eventually get to sending (SMTP) make sure the correct port number is selected and if uses TLS make sure it is correct Port as highlighted in screenshot - also check mark "requires authentication" - this means you will be asked for your mail provider password each time you send an email - this is to prevent someone sending stuff from your computer without your consent.
I installed Thunderbird for a quick test and i added my mail account with the same values as i did in Evolution. It worked out pretty well.
Thunderbird uses probably its own storage for passwords.
Therefore my PC has a problem with the combination of Gnome-Keyring and Evolution. I'm trying now the setup Evolution on my second notebook to see if it fails there too.