The emissions test, or if you have a good OBD2 scanner, then you can:
Check the O2 sensor live data, especially the data of the downstream O2 sensor behind the converter.
And diagnose the converter performance this way.
Here is a link worth reading on that:
OXYGEN SENSORS
If you read there and get or scroll further down you will find a section explaining:
"How does a downstream O2 sensor monitor converter efficiency?"
That link will explain what to look for in the live data on the upstream and downstream O2 sensors. If you do this you will also have to monitor the live data at various driving conditions, especially also under load and the engine needs to be running long enough for the converter to be heated up and reach the proper operating temperature.
If your OBD2 scanner is not capable of presenting live data then you might possibly also be able to get an idea by clearing all the error codes and waiting for your emissions related I/M readiness monitors to be completed after a full drive cycle.
I'm not 100% sure about this at the moment, but I believe one of the I/M readiness test the PCM performs also checks the converter performance and if that passes or fails you would also have a relatively good idea.
The PCM of the 99 Explorer does not have all 11 I/M Readiness tests available and I'd have to look which tests it performs and which not. But if your scan tool shows all the available I/M readiness tests are passed then it should be fine. (But please check back if it really runs a test on the catalytic converter performance.) They can all only either pass, fail, be incomplete, or they are not available.
The conditions necessary for a full drive cycle to be completed and to run and complete all the various tests is described here:
Ford Motor Company Driving Cycle
If you don't have an OBD2 scanner, then you won't really be able to diagnose it yourself.
For a truly complete and fully reliable way to determine you would need professional test equipment with a probe measuring the actual chemical composition of the gases coming out at the exhaust.