I'm currently travelling in Ukraine. So I got myself a new SIM card from the carrier Life
I installed the SIM, made the APN settings, charged the prepay card with money, activated internet, sent out a few SMS messages, updated the weather. And then came the rude awakening: I could not place calls, and I got an e-mail asking what's wrong with my phone because nobody could call me.
I tried to call the carrier's support number, and that didn't work either, except when using the SIM Applications menu item to connect to the call center, that worked. So I knew the hardware is functional, and it had to be something with the SIM or phone settings.
Eventually I stumbled upon the entry Settings > Phone > My Number, which curiously enough is editable. I noticed however that the number was there with the full international area code, but the standard + sign that signifies the international prefix was missing. So I edited my number to include the + sign.
And then a miracle happened: the next instant making and receiving calls worked!
So if you have strange issues with strange SIM cards, be sure to check the non-obvious, and if you have trouble placing calls, check the My Number setting.