We propose to use ferroelectric $(\mathrm{Eu},\mathrm{Ba}){\mathrm{TiO}}_{3}$ ceramics just above their magnetic ordering temperature for a sensitive electron electric-dipole-moment search. We have synthesized a number of such ceramics with various europium concentrations and measured their properties relevant for such a search: permeability, magnetization noise, and ferroelectric hysteresis loops. We also identify and estimate the likely systematics: the magnetoelectric effect, hysteresis-loop heating, and ferroelectric relaxation currents. Our measurements and estimates indicate that a search for the electron electric dipole moment with ${\mathrm{Eu}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{TiO}}_{3}$ could lead to an order of magnitude improvement on the current best limit, if the systematic effects can be controlled.