Couple of things to check:
1. Blades: must be sharp (not razor sharp) and no cracks or damage. Replace if questionable; they are inexpensive can can make a big difference in cut quality.
2. Mower Settings: Depending on the turf, you may need to lower or raise the mower deck a bit to improve suction and cutting performance. Experiment to see what works best for your yard. Some customers report great results with lowering the front 1 notch lower than the rear.
3. Throttle: For the best possible cut, the blades must turn very fast. The engine must be turning at the right speed for this, so make sure the throttle is fully in FAST when mowing. If you're not sure (or your model does not have a throttle) might be worth while to get the engine speed tested (requires a tachometer) and adjusted to the right spec for your mower. Any Honda Dealer can do this for you.
4. Blade Choice: All but a couple of Honda mowers come with twin blades, and they work great in nearly all lawn styles. However, some types of turf where customers want to bag clippings can benefit from removing the twin blades and installing a single, high-lift bagging blade. This provides the maximum suction and can help pull all blades of grass in the right direction. Check with your dealer to confirm which "bagging blade" is correct for your model of Honda mower.
I can help more if you'll share the serial number off the back of the mower deck; it's in the form of "MXXX-1234567" and I can look up some more details for you.
