A method of making RFID devices includes feeding in an interposer web or sheet at a variable (non-constant) speed, cutting single interposers from the interposer web or sheet, and using a rotary transport device to transport the singled (cut) interposers to an antenna web. The interposers are transferred from the rotary transport device and are attached to the antenna web, being operatively coupled to antennas on the antenna web. The interposers each include an RFID transponder chip and conductive leads. A feeder is used to advance the interposer web or sheet into a cutting zone between the rotary cutter and the rotary transport device. The rotary cutting device may be capable of singling multiple interposers at one time, and the system may be capable of thus being able to remove interposers that are not to be joined to the antenna web.