The answer is just use PowerPoint to re-save the emf file:
- Export your emf file 10 times bigger than required
- Drag in into PowerPoint
- Right click image and choose "Size and position"
- Change the scale to 10%**, then on the "Position" tab, set it to be 0cm, 0cm from the Top Left Corner (so you don't lose it off screen). Then press OK.
- Right click this (now correctly sized) image, and choose "Save as picture"
- Save as an emf - it'll be the right size, and still high quality
Note that fonts can really screw up this process. Make sure all your text is outlined otherwise you're likely to run into problems.
** A commenter has found that their emf is about 15% too big when dragged into PowerPoint (so will be 11.5 times bigger instead of 10 times bigger). If you find this, instead of setting the scale to 10%, change the width in PowerPoint to the exact measurement (in cm) that it should be then continue instructions as above. Job done.