Compact microspheres with high-quality (Q) whispering gallery modes are required for many applications involving liquid immersion, such as sensing nanoparticles and studying resonant radiative pressure effects. We show that high-index (1.9 and 2.1) barium titanate glass (BTG) microspheres are perfect candidates for these applications due to their high-Q ( $\sim {10}^4$ in the $1100–1600\mathrm{nm}$ range) resonances evanescently excited in spheres with diameters of $4–15\mathrm{\mu m}$ . By reattaching the spheres at different positions along a tapered optical fiber, we show that the coupling constant exponentially increases with thinner fiber diameters. We demonstrate the close to critical coupling regime with intrinsic $Q=3\times {10}^4$ for water immersed $14\mathrm{\mu m}$ BTG spheres.