Floquet theory combined with a realistic description of the electronic structure of illuminated graphene and graphene nanoribbons is developed to assess the emergent non-adiabatic and non-perturbative effects on the electronic properties. Here we introduce an efficient computational scheme and illustrate its use by applying it to graphene nanoribbons in the presence of both linear and circular polarization. The interplay between confinement due to the finite sample size and laser-induced transitions is shown to lead to sharp features in the average conductance and density of states. Particular emphasis is given to the emergence of the bulk limit response. © 2013 IOP Publishing Ltd.