The magnetic compass is the simplest of instruments! If you would like to save some money and the possibility that your new compass may disappoint, read on!
Try to investigate why there are 2 compasses fitted in the first place. Most unusual! Check to see that the compasses are in good condition and have the fluid with no bubbles. Remove both compasses and use one of them to seek very local cockpit magnetic fields that might have introduced the error in the first place.
If a local magnetic field is present, do something about it! If no local magnetic field, then look and see if there is any form of corrector fitted to either or both compasses, as described by GtE. If neither compass has correctors then re-fit the best for condition and readability. Disregard the comments below only where I write about the correctors.
Choose yourself the most readable compass with correctors then take it to a place free from magnetic anomalies. Point the lubber line at North then South. Trim the N-S correctors to minimise the error. Fit it to the aircraft in such a way that you minimise the N-S error (the 'A' error) then do a compass swing as described by GtE. Small magnetic fields within the airframe are trimmed out using the correctors and you may need to go round the 4 points of the compass twice (or more, depending................ ) because trimming the N-S can have an effect on the W-E, given earth magnetic field influenced by airframe structure.
Once you have minimised errors in N-S and W-E then a calibration swing using 8 or 12 points can be taken. This is where you make out your deviation card and don't touch the correctors.
Fitting a new compass to an airframe with residual magnetism could be a complete waste of money!