We attempted to measure the critical current density Jc of ceramic superconductors with pulsed magnetic fields. Using a pair of search coils coaxially mounted just below a ring sample, we measured induced signals that were considered to be proportional to the time derivative of the sample magnetization. Four samples were used: YBa2Cu3Oy, YBa2Cu4Oy, Bi2Sr2CaCu2Oy, and Bi1.6Pb0.4Sr2Ca2Cu3Oy. These were all synthesized by the polymerized complex method. It was found that the induced signals from the paired search coils are typically of two types. One shows a monotonic decrease to zero as a function of time. The other has a minimum at a certain time and then approaches zero. The observed signals were simulated in the framework of the Bean model and the Kim–Anderson model for critical current density. Theoretical profiles by these two models reproduce the observed results well and suggest that the two types of induced signals are the same in appropriate limits. We discuss how to evaluate Jc from the observed signals.