  Yukawa couplings in the Lorentz- and $CPT$-violating Standard Model Extension
(SME) induce quantum contributions to the electromagnetic moments of quarks,
which are calculated in the present paper and then used to define contributions
to electromagnetic moments of nucleons. High-sensitivity measurements of the
proton and neutron electromagnetic moments then yield constrains on SME
coefficients, reaching bounds as restrictive as $10^{-12}$. This approach
notably grants access to SME effects from the second and third quark families.
