Yeah, I'd imagine that a large part of the problem with that lane combo was Zilean. Garen is quite frightening on his own, but coupled with a Zilean (burst damage and a haste/slow ability), that lane was probably horrifying.
One of the things you can do is attack Zilean if he's following the Garen around. Garen does frightening amounts of damage with his spin, but unless he has exhaust, ignite, and a teammate smacking you, he tends not to kill you with a single spin and silence. His auto-attacks are far less threatening than his spin + silence combo. Zilean, on the other hand, does good burst damage from long range, can speed Garen up (so you can never escape his spin) or slow you down (same effect). He is also, quite unlike Garen, fairly squishy.
Oh, and don't burn your exhaust/slows/etc. on Garen until after he's started spinning (and preferably not until he's under your tower or is about to hit you for massive damage), as the spin removes any slow effects currently on him when it starts.
What champ were you playing, by the way? It really is hard for a lot of melee champs to deal with Garen. That's just how he is.