The accuracy of particle tracking methods for advective transport in porous media depends in turn upon the accuracy of the computed velocity. In many advanced finite-volume methods used in practical applications, the velocity field is often only accurate up to the first order, and is typically defined only on mesh edges. We develop an inexpensive method for reconstructing a quasi-optimal accuracy-preserving velocity field inside the elements of a polygonal mesh. Numerical verification on quadrilateral meshes shows reduction of L (2)-error in comparison with conventional reconstruction strategies.