Focusing on the potential applications of tailored graphene nanoribbons (t-GNRs), in this work, we systematically study size effects on the electronic transport in t-GNR-based molecular junctions. As a result of the manufacturing error generated during the processing or synthesis of t-GNRs using techniques such as ion beam lithography, the final dimensions of the as-fabricated devices often deviate from the design values, giving rise to a size distribution around the mean value which could considerably affect the device performance. To simulate the effects of the manufacturing error, a series of t-GNR-based junctions with various dimensions have been modelled and systematically investigated using density functional theory (DFT) coupled with the non-equilibrium Green's function (NEGF). For junctions that consist of an acene chain connected with two graphene nanosheets, it is found that the chain length has little influence on the electronic transport and that, on the other hand, the junction conductivity is significantly altered by its width due to the different number and nature of the electron transfer pathways. Furthermore, increasing the width of the junction leads to a clear odd-even variation of decreasing amplitude in its transport behavior. These findings underpin further fundamental and device-based studies of t-GNRs.