The charm person spell charms the target "until you or your companions do anything harmful to it". An wizard of the School of Abjuration has a ability called Arcane Ward, which can prevent damage to the wizard by absorbing that damage itself:

Whenever you take damage, the ward takes the damage instead. If this damage reduces the ward to 0 hit points, you take any remaining damage.

Suppose an enemy has charmed an abjuration wizard using charm person, and then that enemy or one of its allies subsequently attacks the wizard, but the Arcane Ward absorbs all the damage of the attack. Does this end the charm spell? In other words, is the act of attacking the wizard (and/or the act of dealing damage to the Arcane Ward) sufficient to break the charm spell, or does the attack have to actually damage the wizard (or cause some other harmful effect) in order to end the spell?

Yes, the Charm Person spell ends

There's some amount of DM discretion here, but I would say in most cases yes. As quoted in the question, Charm Person ends when

you or your companions do anything harmful to the target.

In D&D 5e, words mean what they mean in plain English. "Harmful" in plain English means, "causing or likely to cause harm." Even if the attack ends up being fully blocked by the Arcane Ward (or missing entirely), it was "likely to cause harm" at the time you attempted it.

Another hint to the spell's usage can be found later in its description.

The charmed creature regards you as a friendly acquaintance.

If you do anything that makes it impossible for them to sensibly regard you as a friendly acquaintance, the spell ends (probably - again, at DM discretion).