When intercomparing measurements made by remote sounders, it is necessary to make due allowance for the differing characteristics of the observing systems, particularly their averaging kernels and error covariances. We develop the methods required to do this, applicable to any kind of retrieval method, not only to optimal estimators. We show how profiles and derived quantities such as the total column of a constituent may be properly compared, yielding different averaging kernels. We find that the effect of different averaging kernels can be reduced if the retrieval or the derived quantity of one instrument is simulated using the retrieval of the other. We also show how combinations of measured signals can be found, which can be compared directly. To illustrate these methods, we apply them to two real instruments, calculating the expected amplitudes and variabilities of the diagnostics for a comparison of CO measurements made by a ground-based Fourier Transform spectrometer (FTIR) and the measurement of pollution in the troposphere instrument (MOPITT), which is mounted on the EOS Terra platform. The main conclusions for this case are the following: (1) Direct comparison of retrieved profiles is not satisfactory, because the expected standard deviation of the difference is around half of the expected natural variability of the true atmospheric profiles. (2) Comparison of the MOPITT profile retrieval with a simulation using FTIR is much more useful, though still not ideal, with expected standard deviation of differences of around 20% of the expected natural variability. (3) Direct comparison of total columns gives an expected standard deviation of about 9%, while comparison of MOPITT with a simulation derived from FTIR improved this to 8%. (4) There is only one combination of measured signals that can be usefully compared. The difference is expected to have a standard deviation of about 5.5% of the expected natural variability, which is mostly due to noise.