An increasingly used technique for measuring the thermal conductance of a nanowire is based on a suspended micro-device with built-in resistance thermometers. In the past, the technique has been limited to samples with thermal conductance larger than 1 × 10(-9) W/K because of temperature fluctuations in the sample environment and the presence of background heat transfer through residual gas molecules and radiation between the two thermometers. In addition, parasitic heat loss from the long supporting beams and asymmetry in the fabricated device results in two additional errors, which have been ignored in previous use of this method. To address these issues, we present a comprehensive measurement approach, where the device asymmetry is determined by conducting thermal measurements with two opposite heat flow directions along the nanowire, the background heat transfer is eliminated by measuring the differential heat transfer signal between the nanowire device and a reference device without a nanowire sample, and the parasitic heat loss from the supporting beams is obtained by measuring the average temperature rise of one of the beams. This technique is demonstrated on a nanofiber sample with a thermal conductance of 3.7 × 10(-10) W/K, against a background conductance of 8.2 × 10(-10) W/K at 320 K temperature. The results reveal the need to reduce the background thermal conductance in order to employ the micro-device to measure a nanowire sample with the thermal conductance less than 1 × 10(-10) W/K.