The problem of coupling microscopic and continuum-level descriptions of complex fluids when the microscopic system exhibits slow relaxation times is considered. This type of problem arises whenever the fluid exhibits significant memory effects. The main difficulty in this type of multiscale computation is the initialization of microscopic configurations and establishing the duration of microscopic evolution that has to be computed before a continuum time step can be taken. Density estimation theory is applied to determine the distribution of random variables characterizing the microscopic system. Additional mesoscale equations for the probability density functions required to characterize microscopic states are determined from successive bursts of microscopic simulation. The time evolution of the mesoscale equations is computed using high-order Adams-Bashforth-Moulton predictor-corrector algorithms. The overall computational model is exemplified on a Rolie-Poly fluid. The main benefit of the approach considered here is that the complication of deriving an algorithm for complicated constitutive laws is sidestepped without the need for prohibitively expensive computation at the microscale.