2001 jeep grand cheeroke oil pressure gauge measure high?

This indicates you may have a clog in your system somewhere. Change the oil filter and use a Mopar, Purolator, Or Wix filter and see if this helps. Are you using the correct weight oil. On your Jeep that would probably be 10w20. Using a higher weight could cause this. It could also be the gage is simply wrong. An oil pressure test will verify the accuracy of the gage.