Series of samples of the composition Cu(Y1-xCa x)Ba2Cu3O6+δ (δ ≈ 0.3) have been prepared by a solid-state synthesis route. Precise oxygen content was determined for all the samples by iodometric titration. The c lattice parameter increases with increasing x, indicating successful substitution of Y3+ by the bigger Ca2+ ion. Resistivity (R) versus temperature (T) measurements show that the pristine sample (x = 0.0) is semiconducting down to 5 K. Induction of superconductivity is seen with increasing x. The x = 0.10 sample exhibits the onset of superconducting transition (Tconset) at 42 K without attaining a zero resistance superconducting transition temperature (TcR=0) state above 5 K. For the x = 0.15 and 0.20 samples TcR=0 is observed at 25 and 35 K with Tconset at 52 and 61 K, respectively. DC magnetic susceptibility measurements corroborated the findings from the resistivity measurements. Thermoelectric power (S) measurements in the temperature range of 5-300 K exhibit Tcs=0 at 25 and 35 K respectively for x = 0.15 and 0.20 samples. The room-temperature 5 value decreases with increasing x, indicating an enhanced number of mobile holes. Magneto-transport measurements in applied magnetic fields of 3 and 6 T show a broadening of the superconducting transition. These results will be useful in constructing a more complete phase diagram of the Cu(Y1-xCa x)Ba2Cu3O6+δ system in terms of x and 5.