As I wanted to use both my EspressoBIN boards simultaneously, I unpacked my second micro-USB cable.
I could not get any response from the board when I booted it, so after several attempts, I decided to try the cable I used with the other board.
That cable works.
So if anyone is experiencing problems with the serial console, try a different USB-cable.
Though I live in Denmark, I order my cables from Kenable.co.uk, because they produce their cables themselves; they use pure copper and the cables have a very low resistance.
(I found out after purchasing a bunch of useless cables from China on eBay).
-Thus if you want to be sure you get a good USB-cable or a good Cat6a cable, then I’d like to recommend Kenable, but make sure that you select “Manufacturer=Kenable”, otherwise you might not get the desired quality. (Their “snagless” Cat6a are highly recommendable).