The performance of superconducting RF cavities made of bulk Nb is limited by a breakdown field of Bp ≈200 mT, close to the superheating field for Nb. A potentially promising solution to enhance the breakdown field of the SRF cavities beyond the intrinsic limits of Nb is a multilayer coating suggested in [1]. In the simplest case, such a multilayer may be a superconductor-insulator-superconductor (S-I-S) coating, for example, bulk niobium (S) coated with a thin film of insulator (I) followed by a thin layer of another superconductor (S) which could be e.g. dirty niobium [2]. Here we report the first results of our measurements of field penetration in Nb thin films and Nb-AlN-Nb multilayer samples at 4.2 K using the magnetic field penetration facility designed, built and tested in ASTeC