© 2010-2012 IEEE. Nanometer-thick yttrium iron garnet films, grown on gadolinium gallium garnet substrates by pulsed laser deposition, exhibit remarkably high crystallinity and atomically smooth surfaces. The pseudomorphic growth mechanism leads to large negative out-of-plane uniaxial anisotropy, narrow resonance linewidths, and minimal damping. Magnetic resonance measurements indicate that both the Gilbert damping parameter and inhomogeneous linewidth broadening Δ Hpp,0 are consistently low for films of various thicknesses. Even at film thickness ≈ 20 nm, we attain α 2× 10-4 and Δ Hpp,0 ≈ 1 Oe, which are among the lowest values ever reported.