Levemir is a basal insulin and if you're having short-term issues, that may be an issue with your bolus (fast-acting) insulin.
So I moved from lantus onto levemir just over a week ago and changed unit for unit as I was on split dose, but my sugars are bouncing back and I've had a complete blank as to higher or lower the doses to fix the problem.
It's holding me too high, so I'm dropping to a decent level then an hour later I've shot back up again. I'm on 14 am and 12 pm currently and am too high both am and pm.
If your basal insulin is set perfectly, your levels should remain constant without food.