Solid-state refrigeration using the electrocaloric effect (ECE) in ferroelectric materials is a promising alternative to the conventional vapor-compression technology. In spite of growing interest to the investigation of the ECE, direct measurements of the effect are still rare. In this paper, we report on a modification of a differential scanning calorimeter for direct ECE measurements. The importance of proper estimation of the thermal correction factor and use of proper values of the heat capacitance for correct ECE measurements is discussed. The ECE measurements were performed for Ba(Zr0.2Ti0.8)O3 and Ba(Zr0.12Ti0.88)O3 bulk ceramics. Large electrocaloric temperature changes of 0.54 and 0.34 K are achieved under the application of an electric field of 2 kV/mm for the Ba(Zr0.12Ti0.88)O3 and Ba(Zr0.2Ti0.8)O3 samples, respectively. The relation between the directly measured ECE values and frequently used indirect estimation based on Maxwell's relations is discussed.