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The usual method is to remove metal with a knife or add metal with the copper foil with conductive adhesive. The latter is also soldered around the edges to the original metal.
The microstrip filters I have tuned is done by using small rectangular pieces of pretinned copper foil. Cut some various sizes from a large sheet of petinned copper foil. A good start is to cut pieces having the same width as the microstrip conductors, but at some different lengths. Then use a plastic or wood toothpick and press a piece of foil to the microstrip filter conductors, while monitoring the bandpass response on a scalar or network analyzer. Try different locations of the tuning foil.
In some cases several pieces are required at the same time, this is tricky as most of us just have two hands to hold two ore more toothpicks...
When the best position of a tuning foil is found, just solder it into position. This procedure might require a pretinned microstrip conductor as well for achieving the best solder joint.
Crème de la crème is to provide Cu 'islands' (dots) on the microstrip substrate e.g. at some locations outside the microstrip filter elements, during design of the filter. Then one end of a tuning foil can safely be soldered to these 'supporting areas' and the other end to the microstrip conductor.
Another thing along these lines is to design the filter with margin so that when there are tolerances the filter still works. This requires more elements which will not work for some applications. Make the passband and the stop band wider. Design for less ripple in the passband and more attenuation in the stopband.
If your frequency is not too high, say below 4 GHz, you might try to design the filter slightly too high in frequency. Add a short wire to the hot end of each resonator. Cut the lenght until the filter has reached the desired center freq and passband.
This will only work for tuning a few precent, but I guess that is what you want?
The method was used in VHF communicactions magazine some years ago.
I have tried it to tune a 850 MHz 5 pole harpin filter with great success!
You might want to do some trial and error to get the design process working at its best
But I designed the narrow band pass filter. The filter is sensitivite enough to tune. It is difficult to tune the right coupling cofficient of narrow band pass filter. But all above is not the most hard parts. My system is in the low temperature (77K) and vacuum environment. So hard!!!
A bb glued to a small wooden rod, to run the edge. A razor. Sometimes prepositioned pads, usually wires soldered, then clipped to suit. Always looked terrible.
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So hard!!!