THz pulses are generated from femtosecond pulse-excited ferromagnetic/nonmagnetic spintronic heterostructures via inverse spin Hall effect. The contribution from ultrafast demagnetization/remagnetization is extremely weak, in the comparison. The highest possible THz signal strength from spintronic THz emitters is limited by the optical damage threshold of the corresponding heterostructures. The THz generation efficiency does not saturate with the excitation fluence even up till the damage threshold. Bilayer (Fe, CoFeB)/(Pt, Ta) based FM/NM spintronic heterostructures have been studied for an optimized performance for THz generation when pumped by sub-50 fs amplified laser pulses at 800 nm. Among them, CoFeB/Pt is the best combination for an efficient THz source. The optimized FM/NM spintronic heterostructure on a quartz substrate, having alpha-phase Ta as the nonmagnetic layer, show the highest damage threshold as compared to those with Pt, irrespective of their generation efficiency. The damage threshold of the Fe/Ta heterostructure on quartz substrate is ~85 GW/cm2.