Near-field chipless-RFID tags with high data density and synchronous reading capability are presented and experimentally validated in this paper. The tags consist of a chain of rectangular patches etched or printed at predefined positions on a dielectric substrate, including rigid or flexible (i.e., plastic or even paper) substrates. Patch dimensions determine the binary state, where the larger and smaller patches are associated with the logic `1' and `0' states, respectively, or vice versa. For sequentially and synchronously reading the bits, a sensitive element able to determine the presence of the patches and their size by proximity (through near field using microwaves) is considered. Such element is a microstrip line loaded with a pair of rectangular complementary split ring resonators (CSRRs), one etched inside the other in the ground plane. When the tag chain is displaced at short distance over the CSRRs, the larger patches modify the resonance frequency of both sensing CSRRs, whereas the lower patches do only alter the resonance frequency of the smaller CSRR. Consequently, the ID code is contained in the patch dimensions, and the presence of a patch (regardless of its size) determines the reading times (clock signal), necessary for synchronous reading. Tag reading in this system proceeds by feeding the CSRR-loaded line (reader) with a pair of harmonic signals tuned to the resonance frequencies of the bare CSRRs. Both signals are amplitude modulated (AM) at the output port as consequence of tag motion, and the respective envelope functions contain both the clock signal and the tag ID code. The ID codes of several 16-bit tags, implemented on different substrates (microwave substrate, plastic and paper) and exhibiting a per unit length density of 1.67 bit/cm, have been inferred with the dedicated reader for validation purposes.