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We have used two techniques - the beat spectrum method and the frequency noise spectrum method - to measure linewidths of microelectromechanical systems (MEMS)-based tunable external cavity lasers (ECLs) in the C-band (1527-1567 nm). The two techniques yield similar results, but the latter is able to measure narrow linewidths more accurately in the presence of frequency jitter. The MEMS-based ECL linewidths are found to be inversely proportional to output powers over a wide range of powers. At output powers of 12 dBm, the beat linewidth is no more than 30 kHz, corresponding to per-laser linewidths of about 15 kHz. We show that these lasers are suitable for coherent detection of quadrature phase-shift keying.