The recently discovered (Rb,Cs)EuFe 4 As 4 compounds exhibit an unusual combination of superconductivity (T c ∼ 35 K) and ferromagnetism (T m ∼ 15 K). We have performed a series of x-ray diffraction, ac magnetic susceptibility, dc magnetization, and electrical resistivity measurements on both RbEuFe 4 As 4 and CsEuFe 4 As 4 to pressures as high as ∼ 30 GPa. We find that the superconductivity onset is suppressed monotonically by pressure while the magnetic transition is enhanced at initial rates of dT m /dP ∼ 1.7 K/GPa and 1.5 K/GPa for RbEuFe 4 As 4 and CsEuFe 4 As 4 respectively. Near 7 GPa, T c onset and T m become comparable. At higher pressures, signatures of bulk superconductivity gradually disappear. Room temperature x-ray diffraction measurements suggest the onset of a transition from tetragonal (T) to a half collapsed-tetragonal (hcT) phase at ∼ 10 GPa (RbEuFe 4 As 4) and ∼ 12 GPa (CsEuFe 4 As 4). The ability to tune T c and T m into coincidence with relatively modest pressures highlights (Rb,Cs)EuFe 4 As 4 compounds as ideal systems to study the interplay of superconductivity and ferromagnetism.