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As we know the 1996 car has smaller diameter front brakes 240mm instead of 262mm IIRC, is this a simple bolt on swap like I imagine it should be? What else needs modifying?

I need to upgrade my EJ9 brakes for cheap, preferably stock parts I can find in a scrappy or on ebay. What is my best option and how much can I expect to feel benefit? This is mainly for safety as I often have some pretty close calls breaking for roundabouts and often lock-up since I have no ABS. This lock-up is due to having to stamp on brakes due to not enough stopping power from normal brakes.

I will also bleed system and fill with new fluid but would like to upgrade at the same time.

One good solution will be 262mm discs.
But to make this option to work you will need EK4 front knuckles and calipers or from any other 92-00 civic with 262mm front disc brakes. Even some Ej9s had 262mm front brakes.
With 262mm knuckles you will have a big brake tune variety.
For example 282mm discs from MG ZR160 and calipers from ITR, CRV, HRV, Prelude, EK9, NSX, Legend or Accord.
Then if you have 262mm knuckles you can go further and swap brakes from S2000 or EP3 or Accord typeR 300mm discs.

Thanks for the reply Betek, so 262mm discs from a 1998+ EJ9 will not fit? Okay I will need to get myself some knuckles and calipers from a 262mm EJ9. Anything else I need for the swap (cables, etc) I can get from the EJ9 whilst I am there? Will probably get the front ARB and mounts aswell.

If you gonna swap front knuckles with 262mm discs you will need only the knuckles, calipers, brake pads and discs. Nothing else.
A bonus information --> Even the knuckles from Rover 400 or MG ZS will fit!

i upgraded omp discs 262mm i put ferodo black one the simple , its soft !!! stainless tubes and its feeling is perfect i have the same reaction to every brake action !!!
i could suggest also the ebc green brake pad and and 6.1 motul fluid for more better results

Will I need the 14in wheels for the 262 brakes? Or can I stay with 13in?

You will need 14in wheels with 262mm brake discs

definitely! Imagine that 262mm discs are just about not to fit the stock 14inch rims. They are spacious in 15inch.

Okay I can get some 14in for free so I'll do that. Lots of things to find and order!

One unknown upgrade is to swap discs from Civic CDTi '02-'05, the discs are 260mm in diameter and thickness of discs are 23mm (2mm more than 262mm ej9's discs) and you keep the stock 262mm ej9's calipers with stock ej9 pads.
Or you can either put the CDTi discs and calipers-pads with 262mm knuckles from 1988-2000 civics

The discs on CDTi have thickness of 23mm (on 262mm discs the thickness is 21mm) because the civic CDTi is diesel car which is heavier from usual civics. So that's means CDTi needs more durable brakes from others civics. Also the CDTi discs have better material in discs for durability (more carbon in casting).
I suggest this modification for it's durability and for it's uniqueness.