It could be argued that it's in fact not translated. Or at least, that it's not the choice of some random translator.
The term Noble Phantasm is apparently in the Japanese source material. Mind you, I don't have any of the original material and couldn't read it even if I had it. So I can't confirm any of this firsthand.
But I found a source online quoting the Fate/side material, a 100 pages side book that came out with Fate/stay night, including among other things a sort of encyclopedia.
There is an entry for "hougu" and directly underneath the following
which translates to Nouburu fantazumu -> Noble Phantasm.
So Type Moon chose this as the English reading/translation of "hougu". It seems they did this for many of the terms/names in Fate. Another example is Gilgamesh' Gate of Babylon, which in Kanji is called something like "King's riches".
In this case I would be tempted to actually go so far as to say that Type Moon did not provide a translation into English but rather "coined" the English terms they thought fitting.
It becomes obvious that the literal translation of the kanji into English makes for some lacklustre names. On the other hand some things just can't be properly translated because they don't have same meaning in a different cultural background.
So providing a translation that is not literal but focuses on the concept that you want to convey is a pretty good idea.
I don't know if Noble Phantasm is the best choice but at least the noble part always made sense to me because they are used by heroic spirits. The phantasm part might allude to them not actually being real but sort of a manifestation.
In the Fate/ series they make a point about how much of a heroic spirits power has to do with how famous and legendary they are. Same goes for their weapons. For example, I could mean that Saber isn't using Excalibur but a manifestation of Excalibur based on it's legend.
But only the author can answer what he really had in mind when he chose those translations.