Abstract Non-empirical finite perturbation calculations at the Hartree-Fock, multiconfigurational self-consistent field and configuration interaction levels of approximation are presented for the Fermi contact contribution in multiply-bonded molecules ethene, formimide, formaldehyde, ethyne and hydrogen cyanide. The finite perturbation-multiconfigurational SCF (FPMC) method (with few configurations) is free from the UHF triplet instabilities normally present in single configuration coupled Hartree-Fock (CHF) calculations of the Fermi contact (and spin-dipolar) contribution for π-bonded systems. The behaviour of coupling constants, calculated using FPMC for multiply-bonded systems parallels the behaviour of the CHF coupling constants in comparable systems with single bonds only. The effects of dynamic electron correlations are important and are obtained using the Cl method. After accounting for the orbital contribution by means of the single configuration CHF method, agreement with experiment is excellent for systems containing only carbon and hydrogen, when a double-zeta quality basis set is used. For systems containing nitrogen and oxygen agreement is still reasonable, but the use of larger basis sets seems to be necessary if good agreement with experiment is to be obtained.