We consider synchronization of networks of piecewise smooth oscillators. When dealing with solutions of piecewise smooth systems two main difficulties must be overcome: i) The fundamental matrix solution is not unique in general; ii) The large dimension of the problem requires efficient numerical techniques. In this talk we address both issues. We give a well-defined fundamental matrix solution along synchronous solutions and we use its structure to derive a suitable numerical technique for the computation of the Floquet multipliers of the whole network. This is a joint work with Luca Dieci.