We report in-plane electrical resistivity studies of CeCuBi2 and LaCuBi2 single crystals under applied pressure. At ambient pressure, CeCuBi2 is a c-axis Ising antiferromagnet with a transition temperature [Formula: see text] K. In a magnetic field applied along the c-axis at [Formula: see text] K a spin-flop transition takes place [Formula: see text] T. Applying pressure on CeCuBi2 suppresses T N at a slow rate. [Formula: see text] extrapolates to zero temperature at [Formula: see text] GPa. The critical field of the spin-flop transition [Formula: see text] displays a maximum of 6.8 T at [Formula: see text] GPa. At low temperatures, a zero-resistance superconducting state emerges upon the application of external pressure having a maximum T c of 7 K at 2.6 GPa in CeCuBi2. High-pressure electrical-resistivity experiments on the non-magnetic reference compound LaCuBi2 reveal also a zero resistance state with similar critical temperatures in the same pressure range as CeCuBi2. The great similarity between the superconducting properties of both materials and elemental Bi suggests a common origin of the superconductivity. We discuss that the appearance of this zero resistance state superconductivity may be related to the Bi layers present in the crystalline structure of both compounds and, therefore, could be intrinsic to CeCuBi2 and LaCuBi2, however further experiments under pressure are necessary to clarify this issue.