The only scientifically sound approach I am aware of is to expand space. We know that space is expanding in all directions at a rate virtually undetectable on human scales. If scientists were to be able to identify how this occurs, they might be able to reverse the process locally. Such an shrinking would interact with the world like looking through a lens. If you had a grid of squares 1m on each side and intersected at right angles, and it went through this area, it would appear from the outside as that pocket of space has more grid-squares than the surrounding area.
This counterintuitive result comes because while space is expanding, the laws of physics governing molecular forces aren't. Hubble's Law shows that space is expanding at somewhere around 72 km/s/Mpc. That means two objects that are 1 megaparsec apart find the expansion of space increases the distance between them by 72km/s. One could use these numbers to determine that New York and Los Angeles are separating at a rate of 300um/year due to these effects, but that would not quite be accurate. It would be more accurate to say the points in space where NYC and LA are at this instant are separating at that rate. The actual physical cities don't stay on those points; they move. The distance between them is governed by the molecular forces within the earth. These entities made out of atoms and molecules sort of settle into the expanding space they inhabit. The effects would appear as though there was an ever-so-slight force tugging apart the molecules, but this would be dominated by the inter-molecular forces we know and love today.
So your "shrunk" creatures could simply have had space locally shrunk around them. This would result in there being more apparent space, locally, than there "should" be if you assumed space was flat. They could then go about their merry way, because we didn't change any laws of physics. We just changed the shape of space.
The drawback is that any physical interactions most travel through this field. If you want a Honey I Shrunk the Kids moment when a giant ant terrorizes the heros, do it from afar. As long as the ant is outside of this distortion, it will look gargantuan from inside. However if the ant tries to move to attack the heros, it will have to go through this shrinking space field, and will appear to be the "proper" size for an ant by the time it arrives to bite their heads off.
As an added bonus, you would get an extra check-mark's worth of believability. There are many undeniable effects in physics which are irreversible over the global scale, but are trivial to reverse locally. The march of entropy is, to the best of our knowledge, unassailable globally. However, locally we reverse it all the time. Our refrigerator chills things locally by globally increasing entropy. So it is at least plausible that an expansion of space, which is currently believed to be unabating, could be locally reversed by causing an expansion somewhere else. We don't have any clue how this could be done at the moment, with modern physics, but we didn't understand how heat pumps worked until the mid 1700's either!