I received two beautiful plants as gifts - a deep red amaryllis and red with blue tulips and would like to save them.

Here's what I've done so far. I let them bloom (2x - perhaps 2 bulbs? - for the amaryllis and once for the tulips) Then I cut off the remaining stems. I have not watered the amaryllis since I received it at Thanksgiving and watered the tulips once per week since I received it 3 weeks ago. I live in apartment and have no place to plant them other than the pots in which they were initially planted or another pot purchased for such purpose.

What should I do? Put the pots in a closet? Remove the bulbs and put them in my crisper (far from apples which I know neuter them)? Leave the pots out and water it periodically. Sorry to be dim but I've never tried to save them before.