The role of superstructure finiteness in improving the peak directivity and the directivity bandwidth (DBW) of electromagnetic band gap (EBG) resonator antennas (ERAs) is studied. Simple one- and two-layer superstructures consisting of unprinted dielectric slabs are used for this purpose. In the latter case, each dielectric slab is truncated individually to improve the ERA performance. Initially, existing analytical models that only take into account the reflection characteristics of the superstructure are used to predict the peak obtainable directivity and the directivity bandwidth. Detailed numerical studies are then conducted to observe the validity of these analytical predictions and to study the ERA performance for various finite sizes of the superstructure. It is found that DBW as well as the peak directivity of the antenna is strongly influenced by the size of the superstructure. Moreover, in case of two-layer superstructures, carefully designing each layer to have a different finite size improved the DBW product of an ERA by more than 65%. Experimental results of three ERA prototypes are presented to validate the trends observed in the numerical findings.