Instead of experience, boosting the champion's item level requires the use of the champion armaments up to item level of 900:
Bulky Armor Set: +5 to item level
Spiked Armor Set: +10 to item level
Invincible Armor Set: +15 to item level
Prior to patch 7.2, players could obtain older versions of the items above. These items can only boost the champion's item level up to 850 and they can't be acquired anymore:
Heavy Armor Set: +5 to item level
Fortified Armor Set: +10 to item level
Indestructible Armor Set: +15 to item level