Multi-frequency measurements of the microwave sky can be decomposed into maps of distinct physical components such as the cosmic microwave background (CMB) and the Sunyaev-Zel'dovich (SZ) effect. Each of the multi--frequency measurements is a convolution of the spectrum on the sky with the bandpass of the instrument. Here we analytically calculate the contamination of the component maps that can result from errors in our knowledge of the bandpass shape. We find, for example, that for Planck an

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... nknown 10 band results in a CMB map dT = dT_CMB - 4.3e-3 dT_SZ plus the usual statistical noise. The variance of this contaminant is more than a factor of 100 below the noise variance at all angular scales and even further below the CMB signal variance. This contamination might lead to an error in the velocity of rich clusters inferred from the kinetic SZ effect, however the error is negligible, O(50 km/s), if the bandpass is known to 10 be important for future missions measuring the CMB-SZ correlation.