The d.c. magnetization and magnetic relaxation studies of the calcium doped samples, Y0.95Ca0.05BaCo2O5.5 and YBa0.95Ca0.05Co2O5.5, show the existence of a magnetic glass like behaviour in the family of cobaltites for the first time. Our investigations reveal glass-like arrest of kinetics at low temperature which prevents the system from reaching its magnetic ground state. We show that the low temperature state of these calcium doped phases, which consists of coexisting antiferromagnetic and ferro (or ferri) magnetic phase fractions, can be tuned in a number of ways. Our observations establish that the low temperature state of this oxide is not in thermal equilibrium. The glassy state is formed with the assistance of an external magnetic field, which makes it distinctly different from the more well known metastable state, the spin glass state. The cooling field can tune the fractions of the coexisting phases, and the glass-like state formed at low temperature can also be devitrified by warming the sample. The role of Ca doping in the appearance of these phenomena is discussed in terms of phase separation, involving Co3+ disproportionation into Co4+ ferromagnetic clusters and Co2+ antiferromagnetic clusters.