This paper proposes a method for estimating the lateral position of a tethered multicopter and a method for suppressing wire tension. First, we describe the modeling of a tethered multicopter and catenary theory. Then we show how to estimate the lateral position and tension of the wire tip using catenary theory. Next, we design a position tracking controller for a tethered multicopter. This controller can be used to suppress the effect of the wire tension on the airframe. Finally, to examine the usefulness of the proposed method, we present the results of three types of experiments conducted on actual aircraft: the first is an experiment to verify the accuracy of lateral position estimation, the second is a flight experiment using lateral position estimates, and the third is a flight experiment using tension feedback.