Method and system for making a product (1) having a solid body (2) and having one or more cavities (3, 15) inside that solid body, with a broad surface and a small thickness. A liquid material is provided within a mold (4), and solidification of the liquid material is controlled in a position dependent way from the outside of the product. When using a thermoplastic material, the system may cool said liquid material less in areas that are projections of the cavities on the outside of the product on its broad surface. When using a thermosetting material the system may include means (5, 9) for controlled heating the liquid material, excluding the projections of the intended cavities. Once part of the product has sufficiently solidified outside the intended cavities the liquid material is driven from the intended cavities by means of a fluid. In the product some cavities may be provided with a conductive layer or structure, e.g. applied upon the surface of the relevant cavity, in/on a foam structure (18) or upon the surface of an auxiliary carrier (20) within the relevant cavity.