Rounding a nearly optimal solution to an exact optimal one is well-researched in linear programming, but is not straightforward to do in SOCP and SDP in general, mostly due to the fact that those exact solutions may not be representable with algebraic numbers of low degree. In this talk we discuss the peculiarities of the optimal partition in SOCP and show a few ways to round solutions. Numerical experiments show that these techniques apply to a wide range of problems. In particular, we formulate some conjectures on the convergence properties of interior-point methods applied to SOCPs.