Cat Eats Seedlings

I love my cat Rocket, but he loves my seedlings.

We have a small, crowded house with no room available for special compromises. I have shelves near the window in our living room that looks onto our back yard -- early morning sunshine there. On those shelves I have little lidded greenhouses in which I've potted up seedlings that sprouted in the warmth of the closet where our hot water heater resides. Some of these seedlings need the first phase of hardening off -- removing the lid during the day. But when I do that, dear Rocket has discovered how tasty pine and currant seedlings are. I could just kick him out of the house, but he's only just recently begun considering being a house cat (in the long run it's much better for his health I am sure) plus some days it's really cold out there.

Anybody have any ideas for preventing the cat from eating the plants? I am not able to stay at home and guard them, unfortunately.