Quasi-liquid solid electrolytes are a promising alternative for next-generation Li batteries. These systems combine the safety of solid electrolytes with the desired properties of liquids and are typically formed by solutions of Li salts in ionic liquids incorporated into solid matrices. Here, we present a fundamental understanding of the transport properties in solutions of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Emim][TFSI]), either in bulk form or incorporated in a boron nitride (BN) matrix. We performed a series of quasi-elastic neutron scattering experiments that, given the high incoherent neutron scattering cross section of hydrogen, allowed us to focus on the Emim+ dynamics. First, [Emim][TFSI]/LiTFSI solutions (0.5 and 2.5 mol·kg-1) were investigated and we show how the increase in the concentration reduces the Emim+ mobility and increases the activation energy of their long-range motions. Then, the 0.5 mol·kg-1 solution was incorporated into the BN matrix and we report that the diffusivities of the Emim+ cations that remain mobile under confinement are highly accelerated in comparison with the bulk sample and the activation energy of these motions is drastically reduced. We present the experimental evidence that this effect is related to the content of the Emim+ cations immobilized near the surfaces of the BN pores.