An interposer (110) has contact pads at the top and/or bottom surfaces for connection to circuit modules (e.g. ICs 112). The interposer includes a substrate made of multiple layers (110.i). Each layer can be a substrate (110S), possibly a ceramic substrate, with circuitry. The substrates extend vertically. Multiple interposers are fabricated in a single structure (310) made of vertical layers (310.i) corresponding to the interposers' layers. The structure is diced along horizontal planes (314) to provide the interposers. An interposer's vertical conductive lines (similar to through-substrate vias) can be formed on the substrates' surfaces before dicing and before all the substrates are attached to each other. Thus, there is no need to make through-substrate holes for the vertical conductive lines. Non-vertical features can also be formed on the substrates' surfaces before the substrates are attached to each other. Other embodiments are also provided.