After Perseus killed Medusa, he gifted her head to Athena, who mounted it on a shield and used it in battle to turn her enemies into stone. How did she keep herself from being turned into stone by looking at the shield?
Well, according to Ovid, she din't put Medusa's entire head on the shield, just the snakes from her hair:
Jupiter’s daughter turned away, and hid her chaste eyes behind her aegis. So that it might not go unpunished, she changed the Gorgon’s hair to foul snakes. And now, to terrify her enemies, numbing them with fear, the goddess wears the snakes, that she created, as a breastplate.’
Because Ovid (that translation anyway) says "terrify" and not "turn to stone", it would suggest that Athena didn't actually wear the entire head in her armor, just the snakes; which perhaps on their own didn't turn anyone to stone.
Perseus delaying resolutely, and combining that with calm words. Inferior in strength (who could equal Atlas in strength?), he said, ‘Well now, since you show me so little kindness, accept a gift’ and turning away himself, he held out Medusa’s foul head, on his left hand side. Atlas became a mountain, as huge as he himself had been. Now his hair and beard were changed into trees, his shoulders and hands into ridges. What had been his head before was the crest on the mountain summit. His bones became stones. Then he grew to an immense height in every part (so you gods determined) and the whole sky, with its many stars, rested on him.
Athena probably wouldn't have been turned to stone from Medusa's head since Athena was the one who cursed Medusa to look like that in the first place using her own power. Like if someone tried to use Zeus's thunderbolts against him; I don't think it would work since they are his.