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In this article, we show that the dielectric constant of lead-free ferroelectric ceramics based on the solid solution (1-x)(Bi0.5Na0.5)TiO3-xBaTiO3, with compositions at or near the morphotropic phase boundary (MPB), can be tuned by a local applied electric field. Two compositions have been studied, one at the MPB, with x = 0.06 (BNBT6), and another one nearer the BNT side of the phase diagram, with x = 0.04 (BNBT4). The tunability of the dielectric constant is measured at microwave frequencies between 100 MHz and 3 GHz by a nonresonant method and simultaneously applying a dc electric field. As expected, the tunability is higher for the composition at the MPB (BNBT6), reaching a maximum value of 60% for an electric field of 900 V/cm, compared with the composition below this boundary (BNBT4), which saturates at 40% for an electric field of 640 V/cm. The high tunability in both cases is attributed to the fine grain and high density of the samples, which have a submicrometer homogeneous grain structure with grain size of the order of a few hundred nanometers. Such properties make these ceramics attractive for microwave tunable devices. Finally, we have tested these ceramics for their application as infrared pyroelectric detectors and we have found that the pyroelectric figure of merit is comparable to traditional lead-containing pyroelectrics.