On results day at my school, we were just invited to drop in at any time on a certain day to collect our results; and basically, some teachers were sitting in the maths room which was right by reception. I just went into the reception, got sent to the maths room, had a short chat with the teacher there who had my results(she just asked me whether I was happy with my grades, I said no; she said 'yeah, you could have done better'). It wasn't particularly stressful; and I just walked off afterwards with no fuss. Might be worse if your results are particularly bad. (I got mostly Bs, and I was originally predicted A*s, so my teachers were a bit disappointed but they didn't shame me or anything)
If you ask, they'll probably let you take your results without having to talk to anyone about them, if you're worried about doing badly.