HD 22128 and HD 56495 are both double-lined spectroscopic binary systems with short orbital periods, which have been proposed to host magnetic Ap stars. Ap stars in short-period binary systems are very rare and may provide insight into the origin of magnetism in A-type stars. We study these two systems using high-resolution MuSiCoS spectropolarimetric data, in order to assess the presence of magnetic fields and study the atmospheric chemistry of the components. This represents the first modern magnetic measurements and careful spectroscopic analyses of these stars. We find no evidence of a magnetic field in any of the stars, with precise uncertainties on the longitudinal magnetic field of 50 and 80G in the components of HD 22128, and 80 and 100G in the components of HD 56495. We performed detailed abundance analyses of both stars in both systems, finding clear evidence of Am chemical peculiarities in both components of HD 22128, and in the brighter component of HD 56495, with overabundant iron peak elements and underabundant Sc and Ca. The less luminous component of HD 56495 is chemically normal. The atmospheric chemistry is consistent with the absence of magnetic fields, and consistent with the theory of Am star formation proposing that tidal interactions slow the rotation rate of the star, allowing atomic diffusion to proceed efficiently.