The recently discovered (Rb,Cs)EuFe4As4 compounds exhibit an unusual combination of superconductivity (Tc∼35K) and ferromagnetism (Tm∼15K). We have performed a series of x-ray diffraction, ac magnetic susceptibility, dc magnetization, and electrical resistivity measurements on both RbEuFe4As4 and CsEuFe4As4 to pressures as high as ∼30GPa. We find that the superconductivity onset is suppressed monotonically by pressure while the magnetic transition is enhanced at initial rates of dTm/dP∼1.7K/GPa and 1.5K/GPa for RbEuFe4As4 and CsEuFe4As4, respectively. Near 7 GPa, Tc onset and Tm 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 ∼10GPa (RbEuFe4As4) and ∼12GPa (CsEuFe4As4). The ability to tune Tc and Tm into coincidence with relatively modest pressures highlights (Rb,Cs)EuFe4As4 compounds as ideal systems to study the interplay of superconductivity and ferromagnetism.