You might call it "to swear allegiance." As far as I recall, that's how they did it in Julius Cear's times.

sich mit der geschlossenen rechten Faust als Zeichen des Respekts auf die linke Brust schlagen

to strike one's left breast with one's right fist as a sign of respect

... or, more loosely ...

to show respect by striking one's left breast with one's right fist

The translation is actually straightforward, but I agree with Carly in that "allegiance" might be a better word than "respect" in this context.

Thanks a lot U2 :-)