The Tc of 124 is enhanced by Ca substitution: CaxY(1‐x)Ba2Cu4Oy prepared at 200 bar at 930°C shows Tc = 89 K for x = 0.1. The 124 phase remains stable with Ca substitution at P(O2) ≥ 50 bar. For P(O2) = 2‐16 bar, Ca substitution stabilizes a tetragonal 123 phase CaxY(1‐x)Ba2Cu4Oy, which shows a Tc (87 K for x = 0.2) comparable to that of unsubstituted orthorhombic 123. The synthesis of CaT‐123 has been achieved in oxygen overpressure as small as 1 bar.