In my experience I've found the most effective way of memorizing a piece of music is knowing the note/chord names and how they musically relate to each phrase and section.
Knowing the note/chord names works as a kind of shorthand. In other words, it limits the possibilities to six sounds and twelve notes. Without this limitation, it doesn't take much to become overwhelmed by the seemingly infinite ways a tune can be put together.
For years I fell into the trap of memorizing music by muscle memory alone. At the time I simply didn't have enough experience to see how everything was connected. Muscle memory has its place, but at some point it became painfully obvious to me that muscle memory alone is limited and unreliable.
