The instantaneous linewidth of rapidly wavelength-swept laser sources as used for optical coherence tomography (OCT) is of crucial interest for a deeper understanding of physical effects involved in their operation. Swept lasers for OCT, typically sweeping over ∼15 THz in ∼10 μs, have linewidths of several gigahertz. The high optical- frequency sweep speed makes it impossible to measure the instantaneous spectrum with standard methods. Hence, up to now, experimental access to the instantaneous linewidth was rather indirect by the inverse Fourier transform of the coherence decay. In this Letter, we present a method by fast synchronous time gating and extraction of a "snapshot" of the instantaneous spectrum with an electro-optic modulator, which can subsequently be measured with an optical spectrum analyzer. This new method is analyzed in detail, and systematic artifacts, such as sideband generation due to the modulation and residual wavelength uncertainty due to the sweeping operation, are quantified. The method is checked for consistency with results from the common, more indirect measurement via coherence properties.