Fetch Mac OS
Most of the time, you can re-download the current version of macOS via the Mac App Store, and older ones via these links:
Oct 11, 2020 Operating System: Mac OS X; Users: William & Mary faculty, staff and students only; Cost: Free Trial located on Fetch website; Download Now (52 MB) Company Site; Fetch is an easy-to-use, full-featured FTP and SFTP client for the Apple Macintosh.Please note if Fetch does not work for you, there are other free SFTP programs available on the web.
However, I’ve run into a situation several times where the Software Update mechanism simply refuses to initiate a download:
After entering host name and userid, Mac OS errors are reported before even entering the password. If you then enter the password, Fetch will log in ok, but only if 'Add to keychain' is NOT selected. You can use Fetch, a popular FTP program for Mac OS and Mac OS X, to transfer files to and from a remote computer. For example, using Fetch, you can download a file from an anonymous FTP site. Company Site Fetch is an easy-to-use, full-featured FTP and SFTP client for the Apple Macintosh.Please note if Fetch does not work for you, there are other free SFTP programs available on the web.
Thankfully, macOS installers can be downloaded via Terminal in macOS Catalina. This command will download the most recent version of macOS, depositing it in your Applications folder:
softwareupdate --fetch-full-installer
The softwareupdate
command has some neat tricks up its sleeve, as pointed out by Armin Briegel:
The --fetch-full-installer
flag has a sub-flag: --full-installer-version
which allows you to download a specific version.
During my testing in the Catalina beta version I was able to download 10.15, 10.14.6, 10.14.5, and 10.13.6. I was not able to test if 10.13.6 would download the hardware specific build of 10.13.6 for the 2018 MacBook Pro, since I do not have that hardware.
Fetch Mac Software
So, to pull 10.13.6 down, you’d use:
softwareupdate --fetch-full-installer --full-installer-version 10.13.6
Download Fetch

I wish Apple would just have a support document up with direct downloads for all of this stuff, but this tool is not a bad alternative.
Update: Don’t miss this documentation from JAMF for more on the subject.