We analyze theoretically charge transport in Coulomb coupled graphene waveguides (GWGs). The GWGs are defined using antidot lattices, and the lateral geometry bypasses many technological challenges of earlier designs. The drag resistivity ρD, which is a measure of the many-particle interactions between the GWGs, is computed for a range of temperatures and waveguide separations. It is demonstrated that for T>0.1TF the drag is significantly enhanced due to plasmons, and that in the low-temperature regime a complicated behavior may occur. In the weak coupling regime the dependence of drag on the interwaveguide separation d follows ρD∼d−n, where n≃6.