Quantitative Marxian/Marxist micro and macro economic models?
There is a very interesting paper by John Roemer, published in Econometrica in 1980, that presents a mathematical general equilibrium Marxian model. I am not sure someone have ever estimated it though. Find it here (subscription required).
General equilibrium models (oftentimes idyosincratic) were also developed in the USSR. Check here for an account of them.
Models also informed (or attempted to inform) policy in USSR. The 1985 book "Macromodels of the National Economy of the USSR" gives an account of such models and policy applications.