This study systematically examines the interactions of the trigonal bipyramidal silicon pentafluoride and octahedral silicon hexafluoride anions with either one or two water molecules, (SiF5-(H2O)n and SiF62-(H2O)n, respectively, where n = 1, 2). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using the CCSD(T) ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for Si, O, and F; denoted as haTZ). Two monohydrate and six dihydrate minima have been identified for the SiF5-(H2O)n systems, whereas one monohydrate and five dihydrate minima have been identified for the SiF62-(H2O)n systems. Both monohydrated anions have a minimum in which the water molecule adopts a symmetric double ionic hydrogen bond (DIHB) motif with C2v symmetry. However, a second unique monohydrate minimum has been identified for SiF5- in which the water molecule adopts an asymmetric DIHB motif along the edge of the trigonal bipyramidal anion between one axial and one equatorial F atom. This Cs structure is more than 2 kcal mol-1 lower in energy than the C2v local minimum at the CCSD(T)/haTZ level of theory. While the interactions between the solvent and ionic solute are quite strong for the monohydrated anions (electronic dissociation energies of ≈12 and ≈24 kcal mol-1 for the SiF5-(H2O)1 and SiF62-(H2O)1 global minima, respectively), these values are nearly perfectly doubled for the dihydrates, with the lowest-energy SiF5-(H2O)2 and SiF62-(H2O)2 minima exhibiting dissociation energies of ≈24 and ≈47 kcal mol-1, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -100 cm-1 for the SiF5-(H2O)2 minimum and -300 cm-1 for the SiF62-(H2O)2 minimum relative to an isolated H2O molecule at the CCSD(T)/haTZ level of theory. This work also corrects the OH stretching frequency shifts for two dihydrate minima of PF6- that were previously erroneously reported ( J. Phys. Chem. A 2020, 124, 8744-8752, DOI: 10.1021/acs.jpca.0c06466).