I'm planning on upgrading the front calipers on my 93 coupe to the C5 set-up. At the same time I want to install speed bleeders on all four calipers. The fronts are no problem since I'll do the bleeders befor I install the calipers, but when I do the rears how do I keep brake fluid from spilling all over the garage floor?

As long as you don't apply pressure, you don't lose that much fluid... besides, you do need to bleed them...

I agree with Andy's comments. Little fluid loss should
occur.

To minimize spillage and the adverse consequences that
brake fluid can have on special surfaces, prepare in
advance by cleaning the caliper and laying down some
absorbant material, then work fast.

Use compressed air (if available) and a stiff clean nylon
brush (toothbrush or parts cleaning brush) to clean the
caliper in the area around the fitting.

Corrugated cardboard from a discarded box is useful for
catching drips.

Have the SpeedBleeder near at hand so it can be installed
right after the OEM part is removed.

.

Yep, just screw them in, and then bleed the pass-rear, driver-rear, pass-front, driver-front

You will get a little bit of dribble but no alot.

Thanks to all. I probably won't get to them for a few weeks but I'll let you all know how it turns out.

Also, you may want to remove the factory sealant... depending on what brand you get.

I used Russell bleeders and the sealant was so damn hard it flaked off and got in the bleed port and made my calipers leak.

I fixed it by running them through a thread die and then putting some fresh thread sealer on there. The thread sealer is not for sealing the brake pressure in, it's only for keeping air from being drawn in while bleeding. Note that the oem bleed valves don't need thread sealer.