The aromaticity of cyclic 4n pi-electron molecules in their first pi pi* triplet state (T-1), labeled Baird aromaticity, has gained growing attention in the past decade. Here we explore computationally the limitations of T-1 state Baird aromaticity in macrocyclic compounds, [n]CM's, which are cyclic oligomers of four different monocycles (M = p-phenylene (PP), 2,5-linked furan (FU), 1,4-linked cyclohexa-1,3-diene (CHD), and 1,4-linked cyclopentadiene (CPD)). We strive for conclusions that are general for various DFT functionals, although for macrocycles with up to 20 pi-electrons in their main conjugation paths we find that for their T-1 states single-point energies at both canonical UCCSD(T) and approximative DLPNO-UCCSD(T) levels are lowest when based on UB3LYP over UM06-2X and UCAM-B3LYP geometries. This finding is in contrast to what has earlier been observed for the electronic ground state of expanded porphyrins. Yet, irrespective of functional, macrocycles with 2,5-linked furans ([n]CFU's) retain Baird aromaticity until larger n than those composed of the other three monocycles. Also, when based on geometric, electronic and energetic aspects of aromaticity, a (3)[n]CFU with a specific n is more strongly Baird-aromatic than the analogous (3)[n]CPP while the magnetic indices tell the opposite. To construct large T-1 state Baird-aromatic [n]CM's, the design should be such that the T-1 state Baird aromaticity of the macrocyclic perimeter dominates over a situation with local closed-shell Hiickel aromaticity of one or a few monocycles and semilocalized triplet diradical character. Monomers with lower Hiickel aromaticity in S-0 than benzene (e.g., furan) that do not impose steric congestion are preferred. Structural confinement imposed by, e.g., methylene bridges is also an approach to larger Baird-aromatic macrocycles. Finally, by using the Zilberg-Haas description of T-1 state aromaticity, we reveal the analogy to the Bickel aromaticity of the corresponding closed-shell dications yet observe stronger Hiickel aromaticity in the macrocyclic dications than Baird aromaticity in the T-1 states of the neutral macrocycles.