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EMF is problematic as a mechanism for Equestrian magic because it's a well-understood phenomenon that's limited in its abilities.  Explaining how it could produce matter transformation and teleportation, for instance, would be difficult without serious hand-waving that someone knowledgeable on the topic could probably blow out of the water.  Also, the suggested countermeasure (EMP) is difficult to produce in a reliably controllable manner without bulky equipment and it introduces the constant danger of frying human gear as well as pone horns.  Since the humans only need to manipulate the effect of magic rather than understand it completely, I suggest using a natural phenomenon that is known to, but barely understood by current science -

 - specifically, zero point energy.  Introductory quantum mechanics texts love to freak students out by stating that even bare vacuum is a roiling ocean of potential particle-antiparticle pairs that appear ex nihilo then mutually destroy one another billions of times per second.  All that stops you from spontaneously turning into plasma or your dining room from filling up with goat milk at any random moment is the iron fist of probability.

  The creatures of Equestria have evolved the ability to manipulate this quantum probability, calling matter and force into being from literally nothing.  Pegasi and earth ponies for instance assert the existence of kinetic energy in the form of velocity and muscular force, respectively.  Unicorns and other overt 'magic' users can make a much greater variety of quantum assertions and can do it projectively.  The limitation on Equestrian quantum manipulation is the amount of probability the creature is required to override.  Manipulating X sum of matter and/or energy requires X amount of manipulatory ability, which varies widely.  Rarity's relatively average power can toss around a few clothing dummies or set off a defensive flash-bang, whereas Twilight can levitate a thousand-ton water tower.

The way to neutralize pony magic is to increase the local level of quantum uncertainty to beyond what their assertive ability can handle.  The simplest means to accomplish this is via radioactive decay.  Alpha-emitting isotopes are relatively safe to work with provided they don't get inside you, and each gram of, for instance, Po-210 would add around 2.9x10^21 additional possibilities that the pony has to control.

A riot shield given a polonium-210 powder coat would be very hard for Rarity to get a telekinetic 'grip' on and would protect the wielder from being blasted because her 'blasts' are really assertions about kinetic and/or heat energy existing in the shield and points past it.  Similarly a bullet coated with the same isotope might make it through her shield, though perhaps with greatly decreased speed.   Stopping the blasts Twilight was using to blow man-sized chunks out of solid crystal or preventing her from teleporting out of a room might require inch-thick walls of solid radioactive material.  One of shiny's shields would probably be impervious to anything short of a thorium-filled tank shell.  This mechanic gives the humans the means to counteract magic while still allowing very powerful magical beings to present a believable hazard.

It would be simple to introduce by having Rarity levitate a pistol with tritium sights or a smoke detector or something and remark on the radioactive bit's 'strange slipperiness.'  The humans investigate and discover the radiation link and either do or do not fully figure out how it works, but regardless they know they've found a countermeasure.

Related idea:  perceiving the quantum soup underlying reality is an additional sense that magic-users have and that originates in the horn.  (they would say instead, 'seeing the magical weave')  Covering a unicorn's horn with sufficiently thick radioactive material would completely magically incapacitate them and also likely be disorienting due their sudden 'weave blindness.'

Further thoughts:
1. Teleportation is the quantum assertion that matter exists HERE and not THERE.  Like all horn-based magic it's projective, so probabilistic complexity is increased by distance and intervening matter.
2. Transmutation is the assertion that matter is THIS and not THAT.  Probabilistic complexity is increased by mass and dissimilarity between the old and new objects.
3. Pegasus and earth pony magics are much harder to neutralize with radioactivity because they are simpler in scope and almost entirely instinctive as opposed to an act of will.
4. Exceptionally gifted specimens of non magic-using races sometimes exhibit unicorn-like abilities such as RBD's rainbow trail, Fluttershy's coercive stare and Pinkie's ...well, Pinkie-ness.  Such abilities tend to be accompanied by mental instability like Pinkie's hypermanic nature and Flutters' crippling social anxiety.
5. Based on #4, Derpy Hooves is potentially a spectacularly powerful magical entity, which is possibly why the Doctor keeps sniffing around her in so many fanfics.
6. Wild card possibility:  magical beings whose abilities are inherently chaotic could respond in the opposite manner to increased localized uncertainty.  Dropping Pinkie Pie into a nuclear plant's reactor core would elevate her to Discord's power level.  Dropping Discord himself in there would create a new (and exceptionally ridiculous) God-Emperor.

7. You mentioned wanting a method to increase the potency of magic as well as dampen it.  This idea doesn't contain the means to directly do that other than dipping Pinkie in liquid uranium, but it can be used to assist friendly magic users against hostiles by providing them with radioactive armor and weaponry.