The best way to measure purified invertase is to measure the release of glucose from sucrose. This can be done either by measuring an increase in the reducing sugar, by dinitro salicylic acid for example, or by measuring glucose specifically using an enzymatic assay, such as the glucose oxidase assay.
(Reducing end assay: http://www.eng.umd.edu/~nsw/ench485/lab4a.htm)
However if you are measuring the activity in the honey the background sucrose will be so high it will interfere with the measurements. To partially purify the enzyme from the sugars you can try gel filtration or ion exchange chromatography - you will probably need to dilute the honey to reduce viscosity. The sugars will elute later/ not be retained on the column respectively, leaving the protein in the other fraction.