Aluminosilicate (AS) glasses incorporating rare-earth (RE) elements exhibit favorable mechanical and (magneto)optical properties that reflect their unusual structural Organization. Yet, experimental reports on the local RE3+ environments in AS glasses are very sparse. We examine the Y3+ and Sc3+ cations in Y2O3-Al2O3-SiO2 and Sc2O3-Al2O3-SiO2 glasses of variable RE/Al/Si contents by utilizing magic-angle spinning (MAS) Y-89 and Sc-45 nuclear magnetic resonance (NMR) experiments coupled with density functional theory (DFT) calculations of Y-89/Sc-45 NMR chemical shifts. The DFT models reveal {Y-[p]} and {Sc-[p]} coordination numbers (p) spanning 5 <= p <= 8 and 4 <= p <= 7, respectively; with {Y-[6], Y-[7] and {Sc-[5], Sc-[6]} species dominating. Wide isotropic chemical shift ranges of 35-354 ppm (Y-89) and'48-208 ppm (Sc-45) are observed, as well as sizable shift'anisotropies up to approximate to 370 ppm and approximate to 250 ppm for Y-89 and Sc-45, respectively. Both the isotropic and anisotropic chemical shifts grow when the coordination number p is decreased for Y-89([p]) as well as Sc-45([p]). Second to the coordination number, we demonstrate that the Y-89/Sc-45 isotropic chemical shifts are mainly influenced by the RE/Al/Si constellation in the second coordination sphere of Y and Sc; where the shift tends to increase for emphasized contacts with neighboring RE and Al species at the expense of Si. These DFT-derived trends are corroborated by a progressive 89Y deshielding observed in MAS Y-89 NMR spectra for increasing Y and/or Al content of the glass. We also introduce heteronuclear MAS NMR experimentation involving the pairs of Y-89-Al-27 and Sc-45-Si-29 nuclides, utilized for probing the contacts between the Y3+/Sc3+ cations and the AS glass-network forming groups.