This work presents a method for reducing acoustic resonances in ferroelectric barium strontium titanate (BST)-based bulk ceramic varactors, which are capable of operation in high-power matching circuits. Two versions of parallel-plate varactors are manufactured here: one with pure BST and one with 10 vol-% magnesium borate, Mg3B2O6 (MBO). Each varactor includes a 0.85-mm-thick ferroelectric layer. Acoustic resonances that are present in the pure BST varactor are strongly suppressed in the BST-MBO varactor and, hence, the Q-factor is increased over a wide frequency range by the addition of small amounts of a low-dielectric-constant (LDK) MBO. Although the tunability is reduced due to the presence of non-tunable MBO, the increased Q-factor extends the varactor’s availability for low-loss and high-power applications.