"Effective Mass" can be determined experimentally by following methods as mentioned below.
1. As you have mentioned normally, "Effective masses" were measured using cyclotron resonance, a method in which microwave absorption of a semiconductor immersed in a magnetic field goes through a sharp peak when the microwave frequency equals the cyclotron frequency.
2. Now a days, "Effective Masses" have more commonly been determined through measurement of band structures using techniques such as angle-resolved photo emission (ARPES) or, most directly, the de Haas–van Alphen effect.
3. "Effective masses" can also be estimated using the coefficient γ of the linear term in the low-temperature electronic specific heat at constant volume. The specific heat depends on the effective mass through the density of states at the Fermi level and as such is a measure of degeneracy as well as band curvature. Very large estimates of carrier mass from specific heat measurements have given rise to the concept of heavy fermion materials.
4. As carrier mobility depends on the ratio of carrier collision lifetime to "Effective Mass", masses can in principle be determined from transport measurements, but this method is not practical since carrier collision probabilities are typically not known a priori.
5. The optical Hall effect is an emerging technique for measuring the free charge carrier density, "Effective Mass" & mobility parameters in semiconductors. The optical Hall effect measures the analogue of the quasi-static electric-field-induced electrical Hall effect at optical frequencies in conductive and complex layered materials. The optical Hall effect permits characterization of the anisotropy of the effective mass & mobility parameters.
ANY angular resolved spectroscopy method (XPS, UPS, v-EELS) that measures the dispersion E(k) will do, as the effective mass is effectively the inverse of the curvature of this function!