This work explores the viscoelastic behavior of two types of polymeric foams: an open-cell melamine foam and a closed-cell polyurethane foam. Experimental measurements were carried out on a torsional rheometer to estimate the complex shear modulus as a function of both temperature and frequency. A different and in some cases strong dependence of shear storage and loss moduli upon frequency and temperature was evidenced. The long-term viscoelastic behavior was then identified through the application of the time-temperature superposition principle. A fractional derivative model was properly calibrated to describe the behavior of each foam. This approach enabled two numerical simulations to further investigate the dissipation of mechanical energy. The first simulations explored hysteresis phenomena in cyclic loads in the time domain. The second tests analyzed their vibration damping performances in the low-frequency range. In both cases, only the viscoelasticity of the foam's skeleton was taken into account. The closed-cell polyurethane foam showed a greater ability to dissipate mechanical energy.