The two input stacks to stitch will very likely (almost always) have the same calibration, so it makes perfect sense (and I expected it) that the calibration of, say, the first stack is set to the resulting, stitched stack.

Suppose one has:
ImagePlus imp1 = ...
ImagePlus imp2 = ...
ImagePlus result = ....

Then all the program needs to do
result.setCalibration(imp1.getCalibration());

A warning could be issued if the calibration of the two input stacks are different to each other. Can be easily tested with:

Calibration cal1 = imp1.getCalibration();
Calibration cal2 = imp2.getCalibration();
if (!cal1.equals(cal2)) {
  YesNoCancelDialog yn = new YesNoCancelDialog(IJ.getInstance(), "Warning!", "The calibration of the two input images is different. Proceed to stich anyway?")
  if (!(yn.yesPressed()) {
    return;
  }
}

I guess all other stitching plugins from src-plugins/Stitching_/ package have the same problem.