After almost a year after freshly installing MacOS, the time finally came for me to need the festering pile of ██ that is Microsoft Office 2011. Naturally, something was broken.
The activation screen refused to accept the license key I had used 5 minutes earlier to download the installer, stating that the activation server was temporarily unavailable.
The solution was to look for updates to Office 2011. After the latest update was installed, the key was accepted and my installation was activated. If that doesn’t work, you can always activate it by phone.