I have no idea how long this has been happing for but I have a 4.0L and everytime I get above 3000 rpm the oil pressure goes up to 80 (expected) but once at 4k rpm it goes off the charts (litteraly) past horizontal to about the 4 or 5 o'clock position. We changed oil it did not fix it. What could be the issue and is it worth addressing.

 

Install a Mopar oil pressure sending unit

 

Mine goes to 80 occasionally. Whacking the sending unit or a restart clears it. I think it's the connection. One of these days I should clean it or put on a new one. Anyway, I don't believe the gauge should be able to go past 80, nor should you even have 80 PSI @ 3000 RPM. Your gauge may be broken. Do some testing before shooting the parts cannon.

 

My experience in my '00 XJ was just having it read at about 80 all the time.
Just goes up to that and stays at that reading no matter what RPM.
Replacing the sensor fixed that.
Since this is an easy job I opted to take a chance with the Napa Echlin line one.
Been about 5 maybe 6 years now and all is good so.......
And a couple years ago I finally got around to checking my oil pressure with a mechanical gauge.
I plumbed in some fittings so I could run the mechanical gauge and cluster gauge at the same time when checking.
They pretty much showed the same reading at a very hot idle so.......

 

Had a similar issue a few years back, replaced my oil pressure sender with a NAPA one and have never had a problem. I know some insist that "you must use sensors from the dealer". The only parts on my Jeep that are MOPAR are the ones installed when it was built. Beyond that any part that has been replaced was replaced with whatever brand was available at the time.

I can't see spending the increased money from dealer sourced parts on a 20 plus year old vehicle.

 

It depends on the part. When my CPS crapped out about 2/3 years ago I did not even think twice about buying a Mopar one.
And I work at a Napa. An awkward part to replace, not hard just awkward, and to important to chance it in my book.
Oil pressure sensor on the other hand. Not critical in the short term and takes about 10 minutes so.......

 

First I would replace the oil sender unit and see if that brings the indicated oil pressure more in line with a normal 4.0L. However, if the high indicated pressure turns out to be accurate, that would indicate you likely have a bypass valve stuck in the closed position. You did not indicate what oil you use but a good many of us XJ owners use Rotella T6 5W-40.