Accurate characterization of on-chip devices in the terahertz band has always been a major challenge. Conventional contact probe stages suffer from issues, such as poor repeatability, large signal loss, and low signal-to-noise ratio. The non-contact quasi-optical probe stage reduces the loss and improves the repeatability, but the optical alignment requirements are strict, and the dynamic range of the measurement is usually poor due to the influence of stray light. Moreover, the above two types of systems cannot be easily integrated with cryogenic cooling systems, which limits their application in terahertz astronomical instruments. In this paper, we propose a quasi-optical on-chip device measurement system based on a dual-channel reference method. By the quasi-optical feed and two integrated on-chip detectors, combined with an accurate calibration method of the detector optical received power and an effective dual-channel crosstalk elimination method, the output power ratio of the three-port devices such as coupler and power divider can be accurately obtained in a single measurement. To introduce a broadband coupler with known characteristics, the measurement can be extended to quantify the insertion loss of the device. In this paper, we performed a detailed characterization of the performance of the built system, validated the calibration method used, and provided several examples for measuring an on-chip twin-slot antenna and an on-chip superconducting spectrometer. The results demonstrate good system performance, and the obtained characteristics of these devices have a good agreement with the simulation.