<p>Reducing the thermal noises in microwave (MW) resonators can bring about significant progress in many research fields. In this study, we consider using three-level or four-level systems as “quantum refrigerators” to cool down MW resonators so as to reduce the thermal noises, and investigate their possible cooling limits. In such a quantum refrigerator system, the MW resonator is resonantly coupled with many three-level or four-level systems via two of their energy levels. A driving laser is applied on the multilevel systems, then together with the help of proper optical emissions, the populations of the multilevel systems can be concentrated into their ground states. Effectively that creates a system with zero temperature, which could continuously absorb the thermal photons in the MW resonator. By adiabatic elimination, we give a more precise description for this cooling process. For three-level systems, it turns out a too strong driving laser significantly perturbs the energy levels, which impedes the energy exchange between the multilevel systems and the resonator, and weakens the cooling effect. For four-level systems, by adopting an indirect pump, such an upper constraint for the driving strength can be released. In both cases, we obtain analytical results for the cooling limit of the MW resonator. Based on practical experimental parameters, our estimation shows the cooling limit could reach lower than the liquid helium temperature, without resorting to the traditional cryogenic systems.</p>