Coupling high-quality suspended atomic membranes to specialized electrodes enables the investigation of many novel phenomena, such as spin or Cooper pair transport in these two-dimensional systems. However, many electrode materials are not stable in the acids that are used to dissolve underlying substrates. Here we present a versatile and powerful multilevel lithographical technique to suspend thin crystals, which can be applied to the vast majority of substrate, crystal and electrode materials. Using this technique, we fabricated suspended graphene devices with Al electrodes and a mobility of 5500 cm(2) V(-1) s(-1). We also demonstrate, for the first time, fabrication and measurement of a free-standing thin Bi(2)Se(3) crystal, which has low contact resistance to electrodes and a mobility of approximately > 580 cm(2) V(-1) s(-1).