The restoration of electricity distribution networks determines the switches operations needed to isolate one area of the network under fault in order to minimize operating costs related to the disconnection of loads and the amount of switching in the restorative state. Additionally, the final topology of the restoration must respect the system operational constraints such as the voltage magnitude limits in nodes, the current magnitude limits in branches, the capacities of the feeders and the radial operation of the distribution network. In this context, this paper proposes the development of a methodology based on a mathematical model of mixed-integer second-order cone programming and of mixed-integer linear programming to solve the problem of restoration switching sequence in smart distribution networks. The proposed methodology uses convexification and linearization techniques to obtain both convex models with a good approximation of the mixed-integer nonlinear programming original model. The convex models are robust, generic and flexible and they provide convergence to the optimal solution using classical optimization techniques and commercial computational solvers. The methodology was tested in a 44-node system and in a real distribution system.