Inverse square law: Each time you cut the distance between the mic and the subject in half you gain 6dB of the desired signal while the ambient noise stays about the same (unless it's coming from the same area as the subject).

Directional mics: A cardioid mic has a broad directional pickup pattern. Point it at the subject and point the back at the unwanted noise to increase the separation between the two. A supercardioid or hypercardioid mic has a narrow pickup pattern for even more isolation, but it does have a rear pickup lobe. Put the unwanted noise at about 128 off axis.

Battery powered devices will avoid some kinds of noise problems related to ground loops, but that's in a bigger setup where you have multiple devices connected together. It may or may not apply to places where you have EMF sources, but it can't hurt.

XLR cables are much more resistant to induced noise.

The world's most expensive wireless systems sound almost as good as a cable.