Ion evaporation is an essential step in the formation of charged ions from electrosprays, yet many aspects of the process are poorly understood. The ion evaporation kinetics of the 1-ethyl-3-methyl-imidazolium+ (EMI+) based ionic liquids (ILs) EMI-BF4, EMI-bis(perfluoroethylsulfonyl)imide, EMI-bis(trifluoromethylsulfonyl)imide and EMI-tris(trifluoromethylsulfonyl)methide (EMI-Methide) are studied by tandem ion mobility-mass spectrometry (IMS-MS) of IL nanodrop residues from positive and negative electrosprays of IL-acetonitrile solutions. Two-dimensional (2D) IMS-MS spectra are obtained using a differential mobility analyzer (DMA) coupled to a commercial quadrupole-time-of-flight mass spectrometer. Nanodrops of different charge states (z=1,2,...,10,...) are separated into distinct bands in 2D DMA-MS spectra, allowing for determination of both nanodrop size (radius) and charge. With the exception of negatively charged EMI-BF4, all clusters observed are charged below the Rayleigh limit of both the ILs and acetonitrile, showing that the charge loss mechanism is ion evaporation. Solvation energies, DeltaG, of evaporating ions from acetonitrile are inferred from radius and charge state data. With the exclusion of EMI-BF4 in negative mode (DeltaG>1.84 eV), all are in the 1.54-1.65 eV range, considerably lower than previously reported for tetra-alkyl ammonium salts in formamide. Measured size distributions of EMI-Methide nanodrops agree with those predicted by ion evaporation theory, though with narrower widths observed for doubly and singly charged nanodrops.