At disaster sites, the use of Micro Unmanned Aerial Vehicles (MUAVs) is expected for human safety. One application is to support first-phase emergency restoration work conducted by teleoperated construction machines. To extend the operation time of a MUAV, the authors proposed a powerfeeding tethered MUAV to provide an overhead view of the site to operators. The target application is to be used outdoors, so a robust and simple position estimation method for the MUAV is required. Therefore, in this paper, the authors propose a position estimation method for the MUAV by observing the slack tether instead of using the Global Positioning System (GPS), vision sensors, or a laser rangefinder. The tether shape is assumed to be a catenary curve that can be estimated by measuring the tether's length, tension, and outlet direction. To evaluate the proposed method, the authors developed a prototype of a helipad with a tether winding mechanism for the tethered MUAV, which contains a measurement function of the tether status. Some indoor experimental results proved the feasibility of the proposed method.