TL;DR: Backup App Data\Local\Chromium on your old machine, copy it to your new one and uncompress (in the same place), install Chromium, profit.

With the migration to a new computer, I've managed to keep all my Chromium settings. The steps I did are the following:

  • On the old computer

    1. Note the chromium version you've installed

    2. Go to App Data\Local

    3. Archive the Chromium directory

      Note: this might be huge! To reduce it, clean the Chromium\User Data\Default\Cache

    4. Note the plugins (optional) - this might be useful if you have plugins depending on external apps like 1Password

  • On the new computer

    1. Download and install Chromium. Ideally, the same version as on the desktop.

      Important: Don't launch it!

    2. Copy the archived Chromium from the old computer to the new one

    3. Uncompress it in your new App Data\Local

    4. Launch Chromium

And, voila!

HTH,