The well-known 1964 sheetlet featuring seven men and one woman who perished in the cause of opposition to the Nazi regime bears this legend:
DEM DEUTSCHEN WIDERSTAND ZUM JAHRESTAG DES 20. JULI . 1944/1964
Working out an exact English translation of this is not as easy as it seems, even though the individual words are easy enough. (Incidentally, the second . is an interpunct rather than a full stop - that is to say, a raised full stop, not easy to produce on a PC keyboard.)
Dem Deutschen Widerstand is "The German Resistance", and Jahrestag des 20. Juli is "the anniversary of July 20th". The dates are separated from, though obviously refer to, that anniversary. That leaves us with zum.
The eight people depicted on the stamp certainly exemplify "Dem Deutschen Widerstand", though only three (I suggest) were directly involved in the 20th July Plot (Stauffenberg, Beck and Goerdeler). So how does zum link the two?
Literally the word translates as "to", though even Google Translate offers several German phrases where that is not exactly the case. In English, such a translation would suggest resistance up until the time of the 20th July anniversary, which makes little sense.
The best I can come up with is resistance as exemplified by the 20th July anniversary. But does the word zum carry that shade of meaning?
"Dem" is dative case and should be translated as "to the" or "for the". More fitting should be "dedicated to".
"zum" is simply "at the" or a bit more ornate "on the occasion of"
So I would translate the whole sentence like this:
"Dedicated to the German Resistance on the occasion of the Anniversary of July 20th 1944"
