This paper is concerned with computable estimates of the difference between exact solutions of initial-boundary value problems generated by the Stokes equation and an arbitrary function from the corresponding energy space. They provide guaranteed upper bounds of errors in terms of weighted norms defined on the space-time cylinder where the exact solution is considered. Estimates are derived with the help of techniques based on a transformation of integral identities that was earlier applied (see [Repin, A posteriori Estimates for Partial Differential Equations, Walter de Gruyter, 2008] and the references therein) to the stationary Stokes problem. In this paper, two types of error majorants are derived. They are explicitly computable and contain only global constants. It is proved that the estimates vanish if and only if the functions considered coincide with exact solutions.