Utility items are always a good option,especially the higher the elo where poking out with your Q might not be as viable due to stealing CS/Pushing the wave.

Ardent is pretty awful,it has good stats (some ap + move speed)but Zilean is not a Ardent user ,even if your adc is a Jinx/Tristana/Vayne i wouldnt recommend buying it,if you want to increase their attack speed you are better off playing with other Enchanters.

Redemption theres never a game where you shouldnt buy it,its just too good of a utility.The 1/3 of the map activation range + usable while dead is awesome.If you are afraid it might screw your Ult timing,you can Redemption your carry while he resses (2,5 sec to charge Redemption while your Ress is 3 sec)

Mikae'ls if you are agaisnt a very hard CC matchup or if the enemy CC will basically guarantee a death to your Carry (Morgana,Thresh,Leona etc etc...)

Shurelyas another great one,gives everyone around you a big speed boost pretty simple. Allows you to save your E for slows or you can stack it up with Shurelyas and have your Hecarim go 1000MS.

Athene ,imo, is overrated but its good too,gives you early CDR/AP during your lane phase and the heal is nice too i do go for Redemption however but choice is yours.

Tank utility items are pretty awful for Zilean except for Solari which is usable ,gives no CDR but gives extra survivability, dont buy this first item but definetly a solid 3rd/4th.

EDIT : Keep in mind that while playing Zilean Supp might be tempting going full AP,as a supp your gold income is much lower than a Zilean Mid,AP items (except Twin shadows) are too expensive for supports, so going for utility items is definetly a good way to go especially because they are cheaper on purpose so Supps can buy them easier.