With Herschel, we can for the first time observe a wealth of high-J CO lines in the interstellar medium with a high angular resolution. These lines are specifically useful for tracing the warm and dense gas and are therefore very appropriate for a study of strongly irradiated dense photodissocation regions (PDRs). We characterize the morphology of CO J=19-18 emission and study the high-J CO excitation in a highly UV-irradiated prototypical PDR, the Orion Bar. We used fully sampled maps of CO J=19-18 emission with the Photoconductor Array Camera and Spectrometer (PACS) on board the Herschel Space Observatory over an area of ~110"x110" with an angular resolution of 9". We studied the morphology of this high-J CO line in the Orion Bar and in the region in front and behind the Bar, and compared it with lower-J lines of CO from J=5-4 to J=13-12 and ^13^CO from J=5-4 to J=11-10 emission observed with the Herschel Spectral and Photometric Imaging Receiver (SPIRE). In addition, we compared the high-J CO to polycyclic aromatic hydrocarbon (PAH) emission and vibrationally excited H_2_. We used the CO and ^13^CO observations and the RADEX model to derive the physical conditions in the warm molecular gas layers.