Place 7 clean half pint jars on a rack in a boiling water canner; cover jars with water and heat to a simmer (180°F/82°C). Set rings aside. Heat lids in hot water, not boiling (180°F/82°C). Keep jars and lids hot until ready to use.
Peel fruit; remove white pith and any seeds from each segment. Measure 9 cups prepared segments; set aside.
Combine sugar, orange juice, honey, gingerroot and cinnamon stick in a large stainless steel saucepan. Bring to a boil; stirring until sugar is dissolved.
Add citrus segments to saucepan; return to a boil and boil 5 minutes. Discard gingerroot pieces and cinnamon stick.
Pack fruit into a hot jar to within 3/4 inch of top rim. Add hot syrup to cover fruit to within 1/2 inch of top of jar (headspace). Using nonmetallic utensil, remove air bubbles and adjust headspace, if required, by adding more fruit and hot syrup.
Wipe jar rim removing any food residue. Centre hot lid on clean jar rim. Screw ring down until resistance is met, then increase to fingertip tight. Return filled jar to rack in canner. Repeat for remaining fruit and hot syrup.
When canner is filled, ensure that all jars are covered by at least one inch of water. Cover canner and bring water to full rolling boil before starting to count processing time. At altitudes up to 1000 ft (305 m), process –boil filled jars – 10 minutes.
When processing time is complete, remove canner lid, wait 5 minutes, then remove jars without tilting and place them upright on a protected work surface. Cool upright, undisturbed 24 hours.