Coherent anti‐Stokes Raman scattering (CARS) is a versatile technique for vibrational imaging that can be realized by a simple setup using a single femtosecond laser oscillator. For such a layout, supercontinuum generation in a photonic crystal fiber (PCF) is commonly used to produce a broadband Stokes beam in the so‐called multiplex CARS spectroscopy; accordingly, characterization of the supercontinuum beam is a necessary requirement to perform controlled experiments. In this paper, we first perform simulations and characterizations of the supercontinuum spectra produced by a PCF in conditions encountered in a typical single‐oscillator multiplex CARS setup. Good agreement between the experimental and simulated supercontinuum spectra is obtained in the whole emission band and for different PCF working conditions, by accurate choice of the simulation input parameters and by accounting for the input beam chirp in the numerical code. The influence of PCF working conditions on the CARS signal measured on a reference sample is also shown. To this regard, we also study the long‐term stability of the Stokes beam and of the associated CARS signal, using the Allan variance to determine a limit to the acquisition time in CARS measurements. We show that Stokes and CARS long‐term spectral fluctuations are on a timescale of some minutes in our setup, setting an indicative limit to the practical acquisition time for reliable CARS measurements. Based on this work, good control over the measurement of vibrational bands by CARS microscopy can be achieved in view of optimized performances in specific spectral bands.