Epitaxial strain can unlock enhanced properties in oxide materials, but restricts substrate choice and maximum film thickness, above which lattice relaxation and property degradation occur. Here we employ a chemical alternative to epitaxial strain by providing targeted chemical pressure, distinct from random doping, to induce a ferroelectric instability with the strategic introduction of barium into today's best millimetre-wave tuneable dielectric, the epitaxially strained 50-nm-thick n = 6 (SrTiO3)nSrO Ruddlesden-Popper dielectric grown on (110) DyScO3. The defect mitigating nature of (SrTiO3)nSrO results in unprecedented low loss at frequencies up to 125 GHz. No barium-containing Ruddlesden-Popper titanates are known, but the resulting atomically engineered superlattice material, (SrTiO3)n-m(BaTiO3)mSrO, enables low-loss, tuneable dielectric properties to be achieved with lower epitaxial strain and a 200% improvement in the figure of merit at commercially relevant millimetre-wave frequencies. As tuneable dielectrics are key constituents of emerging millimetre-wave high-frequency devices in telecommunications, our findings could lead to higher performance adaptive and reconfigurable electronics at these frequencies.