I performed this swap on my '86 CRX SI about a month ago. This swap will be a HUGE improvement over your stock system!
What you'll need is the brake system from an '86-'89 Integra. An '86-'89 Integra is mechanically the same as an '84-'87 civic and most parts will bolt right on. You can even get cross drilled rotors for this system if you want, but for a street car, stock rotors will work best (more surface area).
The parts needed from '86-'89 Integra:
Master cylinder (don't bother with the booster, it won't fit on the Civic)
Proportioning valve
Front calipers
Front rotors
complete rear disc assembly
Rear brake hoses
E-brake cables
Rear caliper mounting bracket to rear axle bolts (4 per side)
(get the whole rear axle with a complete brake assembly if you can)
Since you will be putting alot of effort into swapping these parts, I would recommend rebuilding them or at the very least, have your rotors turned.
Tools needed:
32mm socket
10mm tubing wrench
Breaker bar or pneumatic impact wrench
Torque wrench
The usual tools (sockets, open/box end wrenches etc.)
Repair manual (Civic)
Here's what you'll need to do:
Starting with the master cylinder.
You will need to do a little modification to the mounting flange in order to get it to fit. The round cylinder (barrel) on the back of the master cylinder mounting flange is about 1/4" too large in diameter to fit into the booster, so you will need to grind down the "barrel" a little (not difficult). You can then seal the master to the booster using RTV. Another option that I have heard of, is using the master cylinder from an '87 Prelude. Apparently this master will fit on the Civic booster without modification (I have not tried this yet, so I can't tell you if this really works or not, but as long as the Prelude booster has a 7/8" bore, in theory it should work).
Replace the Civic brake proportioning valve with the Integra unit.
Next, Jack up the entire body of the car SECURELY!!!!! Support the rear axle and remove the wheels.
The front brakes are really easy, just replace the Civic parts with the Integra parts.
The rear brakes are a little more involved, especially the passsenger side (assuming you are in the U.S.). Before you get started removing parts, remove the bolts that hold the bottom of the rear struts in place, this way the torsion on the rear axle will not be fighting against you.
The rear drivers side:
Remove the old drum, hub, brake mounting plate, E-brake cable and brake hose from the Civic. What you will be left with is a spindle and four bolts. You will need to remove these bolts and replace them with the same (longer) bolts from the Integra. The reason for this is because the Integra caliper mounting bracket is much thicker than the Civic brake backing plate.
Next dismantle the driver side brake set up from the Integra. Remove the caliper, rotor, hub, dust shield and caliper mounting bracket untill all that you are left with is a spindle. Toss the Integra spindle and trailing arm in the trash pile since you will not be able to use them (the Integra trailing arms are shorter than the Civic arms).
Install the four bolts (mentioned earlier) from the Integra axle into the Civic axle, then install the, caliper mounting bracket, dust shield, hub, rotor, and caliper.
The rear passenger side:
Remove all parts from the Civic the same as the drivers side. The only difficult part is dismantling the Integra parts. To do this you will need to break apart the Integra swing bearing. This is because the caliper mounting plate is mounted behind the bearing on the Integra (not so with the Civic).
Back to the Civic.
Remove the four bolts around the spindle. You will need to rotate the spindle in order to get them out, as you remove them you will bend the dust flange a little but don't worry about it just bend it back into shape with a flat screwdriver after you have installed the Integra bolts.
Next, install the Integra bolts, straighten the dust flange and assemble this side the same as the drivers side.
Torque down the spindle nuts and stake them.
Install the Integra rear brake hoses:
They are a little longer than the Civic hoses were, so you will need to route them in a way that takes up some slack. Mine ended up in sort of an "S" shape.
Install the Integra E-brake cables:
You will need to use the Civic mounting tabs, so carefully cut the rubber tabs off of the integra cables. These cables are also a little longer than the Civic cables, but you can still route them the same way. The only difference is that I ended up crossing them over underneath the car and installing the left cable to the right side of the E-brake handle and the right cable to the left side, just to take up a little excess length.
Next look around the car and make sure that everything is installed, tightened and bolted down (like the rear strut bolts and hub nut dust covers etc.).
Bleed the brakes.
Adjust the E-brake
Then install the wheels and take it for a test drive!
Note:
It is very important that you DO NOT mix the Civic and Integra brake parts. For example, don't swap the rear disc brakes onto your Civic but leave the stock Civic calipers on the front. Or, DO NOT swap all the disc brakes on to your Civic without swapping the Master cylinder and proportioning valve. This is because the ammount of pressure needed to operate the Integra 4 wheel disc brake system is FAR MORE than the ammount of pressure required to operate the stock Civic drum system. The Integra brake system was designed and balanced at the factory for safe operation, so don't mess with it unless you have a thorough understanding of fluid dynamics!
I'll keep an eye on this thread, but Email me if you need help or have any questions.