In this Letter, we demonstrate theoretically that electromagnetic waves can be "squeezed" and tunneled through very narrow channels filled with epsilon-near-zero (ENZ) materials. We show that the incoming planar wave front is replicated at the output interface, independently of the specific geometry of the channel. A closed analytical formula is derived for the scattering parameters of a particular class of geometries. It is discussed that in some cases the isotropy of the ENZ material may not be an issue. A metamaterial realization of an anisotropic ENZ material is suggested and numerically studied.