Recent developments in the field of magnetic metamaterials have shown that coupled resonator structures can manipulate magnetic fields on a scale shorter than the wavelength of the electromagnetic radiation [E. Shamonina, V.A. Kalinin, K.H. Ringhofer, L. Solymar, J. Appl. Phys. 92 (10) (2002) 6252]. Major improvements in the sensitivity of such devices could be achieved by fabricating the resonating elements from high temperature superconducting (HTS) films on appropriate dielectric substrates. In order to produce a stack of superconducting/dielectric resonator structures, the ideal method involves patterning them into an HTS film grown on the curved surface of a dielectric cylinder. We report here our initial attempts at the growth of Tl2Ba2CaCu2O8 (TI-2212) thin films on the surface of LaAlO3 and MgO single-crystal cylinders. We have found that TI-2212 thin films grow epitaxially on LaAlO3 cylinders with TI-2212 [001] aligned with the closest LaAlO3 pseudocubic [100] direction, resulting in abrupt changes in TI-2212 plate orientation at four positions around the cylinder. In contrast, TI-2212 films grow smoothly on MgO cylinders, with TI-2212 [001] aligned roughly parallel to the surface normal at all positions around the cylinder. This smooth growth on MgO leads to higher critical current values than epitaxial growth, making HTS on MgO a promising candidate for metamaterial device applications. (C) 2008 Elsevier B.V. All rights reserved.