Magnetic shields of various high-temperature superconductors, YBa2Cu3O7−x (YBCO), YBa2Cu3O7−x-Ag composites (random inclusions as well as non-random coatings) and Bi2Sr2Ca2Cu3Ox (BSCCO) were prepared by uniaxial as well as isostatic compression with various dimensions. The shielding properties were measured at 77 K for dc and ac magnetic fields in the range of frequencies from 100 Hz to 10 kHz. The critical penetration field (CPF), defined as the value of the applied magnetic field at which a detectable field was observed inside the cylinder, varied from cylinder to cylinder and also with the ageing of the cylinders in the case of YBCO shields. The highest value of CPF was 16 G at 77 K for YBCO shield prepared by isostatic compression. Even though the stability of BSCCO shields with respect to ageing is good, the CPF values are very low compared to those for YBCO. Detailed studies were performed in the case of YBCO shields. The CPF decreased as a function of time over a period of 90 days. The CPF decreased as the frequency of the applied field was increased. The wave form of the field inside the pot for a sinusoidal applied field was highly distorted and showed the presence of higher harmonics with appreciable amplitude. The wave form was Fourier-analysed to yield the field inside the shield along with the harmonics. The shields with Ag addition seem to give better performance at high fields.