NEVER use volume measure for dry items, even sugar... Always go by weight of item...
That being said, honey is sold by weight, not volume. Also, honey is ~80% sugar, so you need to use 1.25x the weight of sugar in honey... So, if something calls for 8 ounces of sugar (1 cup [water] liquid weight), you would use 10 ounces of honey. I would suggest weighing the sugar you were going to add, and then use that to figure out how much honey to add for a replacement. If you don't have enough sugar on hand for the full cup measure, you'll need to either wing it, or figure something out.
Typically, you add honey (or even sugars) in pound increments. The only times I would add less than a pound of either, is if that's all I have on hand, or if it's for carbonation.
In a brew, I don't see much difference between adding less than a full pound of honey, and a full pound. Less than 1 pound in 5 gallons of wort won't really do all that much. 2-3 pounds of honey starts to become noticeable, with more [obviously] more so...
If you're looking to add this for flavor as well as just yeast food, then do so when the wort has chilled to below 110F (under 100F is even better)... Otherwise, a lot of what gives honey it's flavor will be gone. This is one of the reasons why mead makers often go with the 'no heat' method...