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The James Webb Space Telescope (JWST) will revolutionize the field of high-contrast imaging and enable both the direct detection of Saturn-mass planets and the characterization of substellar companions in the mid-infrared. While JWST will feature unprecedented sensitivity, angular resolution will be the key factor when competing with ground-based telescopes. Here, we aim to characterize the performance of several extreme angular resolution imaging techniques available with JWST in the 3-5 micron regime based on data taken during commissioning. Firstly, we introduce custom tools to simulate, reduce, and analyze NIRCam and MIRI coronagraphy data and use these tools to extract companion detection limits from on-sky NIRCam round and bar mask coronagraphy observations. Secondly, we present on-sky NIRISS aperture masking interferometry (AMI) and kernel phase imaging (KPI) observations from which we extract companion detection limits using the publicly available fouriever tool. Scaled to a total integration time of one hour and a target of the brightness of AB Dor, we find that NIRISS AMI and KPI reach contrasts of $\sim$7-8 mag at $\sim$70 mas and $\sim$9 mag at $\sim$200 mas. Beyond $\sim$250 mas, NIRCam coronagraphy reaches deeper contrasts of $\sim$13 mag at $\sim$500 mas and $\sim$15 mag at $\sim$2 arcsec. While the bar mask performs $\sim$1 mag better than the round mask at small angular separations $\lesssim$0.75 arcsec, it is the other way around at large angular separations $\gtrsim$1.5 arcsec. Moreover, the round mask gives access to the full 360 deg field-of-view which is beneficial for the search of new companions. We conclude that already during the instrument commissioning, JWST high-contrast imaging in the L- and M-bands performs close to its predicted limits.