The CATalyst exhaust converter : (aka: Catcon's, or just Cats) 
Suzuki calls it, a TWC, a Three Way Cat.

You are here, because:
Smog failed, engine don't start, or lost 1/2 the  engine power?,
or were doing the compression test and wanted to complete the job, and make sure the engine can actually breath.

A  Short cut to blockage:
A clogged Exhaust Catalyst Unit ,will a cause power loss, usually at very heavy loads and/or  high speeds.  [ caused by running car with dead sparkplug, stuck open injector and the CEL lamp flashing all the time 1996+ cars flash as a warning, Cat death eminent]

There are 6 to 7 tests depending on the year, or reason to be here
I'll post the obvious first. (the 8th test , really)
  • If you think it's melted inside, and don't have the tools?  for #5
  • You can drop the CAT, start car, see of full power returns,  your neighbors will love you.  ( but most 20 year old cars, the studs snap off, and now 2 problems)
  • You can rack the exh. manifold back, lossen all the bolts such that there is a 1/8 to 1/4" gap under the heads, then rack it back, the ports are all open , start car and test.
No order here, but #5 is my way, if doing cat back exhaust, I never fail to do #6, "targets of opportunity" The vacuum test finds the really super clogged CATS fast)
  1. Four Gas Analyser that most major shops own, follow the manual for gas mix on the hot engine.  (fails smog?)  The Gas test don't lie.
  2. Vacuum drop test, see below.
  3. Pyrometer or IR gun heat test,  just measure the temperature on both sides of the CAT and the output must be 100 deg F.More  that the input to the CAT. If equal or less, the CAT is bad.
  4. 96 or newer car will set  a P0420 failure DTC code. (means bad CAT or running way too rich,, for the test to be valid) See SCOTTY fix his , 2 easy ways.
  5. Do a Oxy O2, sensor front , backpressure test.  See below. Using this tool.     ( the 02 don't come out, well I guess you skipped the 100k service?)
  6. Remove cat and look inside to see if it is melted. The look test. Some can only be seen from the rear,  I drop the muff, and look behind CAT. (yes,   flash light !)  If looks melted it is.  Good looks are , it looks sorta like a bee's honey comb, if it looks like melted comb, it's bad.  Some see no honeycomb at all, its all gone.  ( oops ,EGR is now dead too)
  7. Differential pressure guage test ,  a good test but puts holes in the header pipes. ( some shops are set up to do this fast  (on 96_ cars there are 2 oxy bung test ports. here.)
Many CATcons are replaced and are perfectly good.

Differental Test:
This unit can be tested with a differential pressure gage, at most professional shops.  ( read the instuctions that come with the unit, )  Over kll, IMO.

Vacuum: test:
There is a simple intake manifold vacuum gage test for finding a clogged CAT.  (connect it  to the Evap nipple on the intake manifold)
Ok , here is a hint,  gun the engine and then cut the throttle to idle, then if you notice the vacuum taking forever to return to the correct high value 20inches, then the CAT is clogged.

Oxygen sensor Front B1S1 on this car, we can connect a low pressure , pressure gauge ( some vacuum tools (most) have this built into the unit.
Attach a rubber nose cone adapator to the gauge tube end and insert this cone into the OxyGen sensor bung hole (sensor removed)
start car and do not warm it up , just get an idle and 2500 -3000 rpm reading.

Unplug the Oxygen sensor from its forward bung, and place a pressure gage (0-10 lbs) and expect only 3 -5 PSI back pressure when reving the engine to 2500 RPM.
Most carb vacuum guages have a 0-7 psi pressure section, use that !  All auto stores sell the cheap simple gauge. buy one , and use it.
Many test centers claim 3-5psi max (generic spec.) at 2500 rpm. ( out of gear)
FSM:  (out of gear )
States: 2.8 psi max 2500 RPM (1989 first pub. date, in SUZ.)  and other newer years, 2 psi max.  (I'd go with 2 psi max.) At the 0 senor BUNG.

A quote from:
Once you've made your connection, start the engine and note the backpressure reading. Depending on the application, the amount of backpressure that's considered "normal" will vary. On some vehicles, backpressure should read near zero at idle, and should not exceed 1.25 psi at 2,500 rpm. Others can handle 0.5 to 1.25 psi at idle, but should have more than 4 psi during a snap acceleration test.

Keep in mind a CATcon breakup can dump the alumina material into the muffler and clog it !  Careful testing will reveal this fact.
See , no need to pull it all apart (the piping). ( extremely difficult that is (with siezed nuts ,etc), and is the last resort).
Just PULL THE 02 and test the pressure.
See here for more blockage tests.

Cat killers:
Rich Air/fuel mixtures and lots of air , will kill it dead ( and plug it up).    CEL lamp flashing means, the engine is killing the CAT !!!
(rich A/F only, will  not kill it , it needs oxygen to do that)
Lean causes the CAT to just stop working   (it does not light off), but driving in limp home or any retarded timing (ign) condtion will melt a cat in short order.

The Cat element inside can actually melt and sag, this will clog it up.  It can be extreme this condition.
Driving any Sidekick that gets 15-20mpg will melt the cat.  (This happens in limphome mode or the more worse BACKUP mode of the ECU)

Read the very good document about Catcons:

My Quick CatCon test , using a simple vacuum guage: ( cheap , fast and effective, and no burned fingers)
  1. Warm up and idle engine.
  2. Plug a Vacuum guage into any plenum vacuum port , do not create any leaks.  (my Vac. at idle is 19 inches of Mercury 19 HG.)  I use the EVAP port. Do not use the EGR port.
  3. Race engine to about 2500 RPM, and record the vacuum.  ( if vacuum is significantly lower at 2500 than idle Cat is bad [or exhaust blockage]).
  4. Now slam the throttle shut fast, to idle.  Observe Guage action.
  5. The vacuum should instantly raise about 5 HG above #3 reading and then drop to Idle vacuum observed at #2.   ( if not , suspect CAT blockage ,or more rarely muffler blockage)
  6. Many  say this is one of the most accurate tests for a CAT.  
  • Cat melts down (caused by a gross  too lean or too rich condition) and plugs the CAT.
  • CAT breaks up to chunks and clogs up the muffler,
  • The front pipe on only16 valve engines 92-93 , collapes inside (see TSB all about this).  or someone puts an old pipe on a new car, 92-95 are the suspect years, in truth.
  • Offroad exhaust damage (crushed tubing.)
I like the Vacuum test and the Oxy B1S1 bung pressure test.

One last trick, is to just pull the front O2 sensor, then drive and see if the gross power loss is reduced. (proving a Melted CAT) {or bad 02, sigh, see best way below..)
Do not run car like this , in this state , O2 removed , inside any garage or parked on any snow bank (snow cover ditch, or the like).  
Only a short test, in clear open spaces.
Carbon Monoxide is the silent killer. 

Catcon (CAT) clogged , melted test.
An ASE Excerpt:  (my red marks)
ASE A8, Engine Performance manual, page 60, reference states:

"To check for a restriction in the exhaust, attach a vacuum gauge to the intake manifold and run the engine at approx. 2000RPM, observe the vacuum gauge as the engine is allowed to quickly decelerate.

If the exhaust is FREE of restriction, the vacuum gauge reading will increase immediately upon closing of the throttle, then settle down to a normal reading. If there IS a restriction, the needle of the gauge WILL NOT show an increase." (due to huge backpressure at the exhaust ports)

This is logical if one sees the engine as a air pump that happens to have gasoline pouring into it, the action of the pistons creates a movement of air at the intake ( vacuum) and pushes it out of the exhaust ( pressure) if the exhaust is plugged or restricted, then the vacuum will not increase.

Another way to check for same is to attach a pressure gauge at the after cat O2 sensor port ( if so equipt), a normal reading will be around 2psi at idle and 3 psi at 2K RPM.
The best way is to drop CAT front flange (1/2" gap) and drive. drop header flange or rock back the whole Exhaust manifold from head,  back bolts out 1/2 way.

On can connect OBD2 full scan tool and examine the baro sensors.
On 8v cars this is the MAP sensor.
On 16v this will be EGR MAP ( located top rear of plenum chamber)
These electronic MAP sensors will show the same effect stated above, with no need to connect anything but a scan tool.