The effects of ethynyl substitution on the electronic structure of cyclobutadiene are investigated in this work. Ethynyl substituted cyclobutadienes may be involved in Bergman cyclization reactions and are possible intermediates in the formation of fullerenes and graphitic sheets. Prediction of the electronic structure of cyclobutadiene is challenging for single-reference ab initio methods because of Jahn-Teller distortions and the diradical character of the singlet state. The equation-of-motion spin-flip coupled-cluster with single and double excitations (EOM-SF-CCSD) method accurately describes diradical states and is used to determine vertical and adiabatic singlet-triplet energy splittings in the substituted cyclobutadienes. The adiabatic singlet-triplet gaps decrease upon substituent addition, but the singlet states remain lower in energy. However, the results are affected by spin-contamination of the reference state and deteriorate when an unrestricted HF reference is employed. Additional insights in the electronic structure of cyclobutadienes are obtained by analyzing natural charges and spin densities. The substituents pull the charge out of the cyclobutadiene ring; however, the natural charges and spin densities are found to be nearly independent of the geometry and spin state.