Master Equations and Operator Sum Form I'm more of a quantum optics guy than a quantum info guy, and deal mainly in master equations. I'm interested in operator-sum form, and I'd like to derive the errors in this form for a small quantum system that I'm simulating.

The catch: The quantum system is driven by an external (classical) field modelled with a sinusoidal function, and the damping rates are low, so I can't make a rotating wave approximation to eliminate this time dependence. Given that I must solve the master equation numerically by integration, and the result of each integration at time $t$ is not sufficient information to figure out these errors, and I need to do some work to recover the superoperator matrix that has operated on a vectorised density matrix. i.e. I feed the master equation a vectorised density matrix with a single entry of 1 and the rest zero, and build the matrix like that for a particular time $\tau$. Am I on the right track here (sanity check)? More explicitly, if $\mathrm{vec}(\rho_{ij,t=\tau})$ is the vectorised (so it's a column vector) form of a density matrix with a single entry of 1 in position $i,j$, at $t=0$ that has been evolved to time $\tau$, then a matrix to take the vector form of the density matrix from $t=0$ to $t=\tau$ is given as $\mathbf{M}=\sum_{i,j}\mathrm{vec}(\rho_{ij,t=0})\mathrm{vec}(\rho_{ij,t=\tau})^\dagger$.

The question: Given this superoperator $\mathbf{M}$ that does $\mathbf{M}\,\mathrm{vec}(\rho_0)=\mathrm{vec}(\rho_\tau)$, how can I get Krauss operators for the operator-sum equivalent of $\mathbf{M}$ that are in a useful form? i.e. the system in question is a qubit or a qutrit and another qubit or qutrit. I'd like to be able to do the operator sum in the form of tensor products of spin matrices on each channel if possible.

Side question: Is $\mathbf{M}$ a Choi matrix?

Final note: I awarded the acceptance to Pinja, as I used the paper Pinja suggested. I have provided an answer myself below that fills in the details.
I worked on a very similar problem on my Masters thesis, in which I studied the non-Markovian dynamics of a driven qubit in a dissipative environment. My interest was in checking that the master equation I obtained was completely positive, but this is just one side of your problem. The question turned out to be very non-trivial if no RWA is made, but I was able to get some results using Ref. [J Mod. Opt. 54, 1695 (2007)] and exploiting the fact that the qubit is weakly coupled to the environment. I'll beat my drum and also give the Ref. to an article where I present some of these results, [P. Haikka and S. Maniscalco, Phys. Rev. A 81, 052103 (2010)], you may find it useful.