After losing a toothpaste cap down the sink, I decided to create a screen to catch objects, but still allow water drainage. The design is parameterized so you can use OpenSCAD to generate a drain screen personalized to your sink configuration. It consists of a top plate with square holes in it, and a short sleeve that fits inside the inner diameter of the drain pipe and centers the screen.

Note that on my poorly tuned MakerBot, producing a fine rectangular grid is very tough, so the default grid is quite coarse. (Even that did not come out so great.) MakerBots tuned for fine detail or bigger screens will probably have more successful prints.

Your drain is probably not the same size as mine, so the attached STL file is just for illustrative purposes. I would not suggest using it directly.

1. Download OpenSCAD file.
2. Set plate_diameter to be larger than your drain pipe, but not so large the screen will not sit flat in your sink.
3. Set sleeve_outer_diameter to be a little less than the inner diameter of your drain pipe.
4. Set square_hole_size and square_hole_spacing for your desired grid. Note that very fine grids will probably not come out right.
5. Print. I have not built a heated build platform yet, so I print this with a raft and trim the holes. Raftless is probably the way to go, though.
6. Stop losing razors and caps down the sink!