View source for Masamune (Reaction to Magus)

===Reflexive Power===

''Andrelvis, razor's edge, V Translanka''

The Masamune is said to depend on the user, not its inherent strength as a sword. It also has a spiritually reflexive nature, evident in its corruption of users in Chrono Cross and its enhancement at Cyrus's grave. When Frog battled Magus, his spirit and many feelings sufficiently fortified it to do extra damage, as he was very motivated. The same mindset allowed Frog to split the Magic Cave with the empowered blade. Frog doesn't hate Lavos and other monsters; he rationally knows that Lavos will destroy the world and must be destroyed before he does so, but there is no personal hatred. Whereas, with Magus there is. Magus killed Frog's best friend. So, there's a huge emotional difference between fighting the two...And the Masamune is based on people's emotions and feelings, not their convictions. As dream beings, Masa and Mune are enriched by the potent desire and will of their wielder.

Masa: Quite. I guess it means that a Hero's power comes from within.
Mune: Mucha metaphysical, man.
Masa: Like, MIND over matter, Mune!
Frog: My... mind?

Magus seems to be quite shocked that the Masamune is hurting him so. The Masamune didn't seem to help Cyrus and Glenn 10 years earlier when Cyrus was killed. This implies that the Masamune was powered by Frog's will, otherwise it would have worked when wielded by Cyrus. This could be an example of the Dreamstone being utilized in a way not Lavos-related, since it was Frog's dream to defeat Magus and thus avenge Cyrus.

The Hero's Medal (and later, the Shield and Prop Sword in Chrono Cross) also seem to grant psychosomatic powers (unless Cyrus actually imbues the wearer with spiritual fortitude). This means that in simply wearing and wielding these weapons, the user is much more confident and sober in battle.

This theory fails somewhat to take into account the legend surrounding the sword (that only it can defeat Magus), but given the blade's reflexive nature as evidenced in Chrono Cross, this may only be circumstantial.