We　propose　a　protocol　for　the　generation　of　NOON　states　of　resonator　modes.　The　physical　model　is　composed　of　two　Kerr-nonlinear　resonators　and　a　four-level　qudit.　Using　the　off-resonant　couplings　between　the　resonators　and　the　qudit,　qudit-level-dependent　frequency　shifts　on　the　two　resonators　are　induced.　The　frequency　shifts　allow　us　to　drive　different　resonators　to　the　N-photon　state　when　the　qudit　is　in　different　intermediate　levels.　Consequently,　the　generation　of　NOON　states　with　arbitrary　photon　number　N　can　be　completed　in　only　three　steps,　i.e.,　driving　the　qudit　to　a　superposition　state　of　the　two　intermediate　levels,　driving　one　of　the　resonators　to　its　N-photon　state,　and　driving　the　qudit　back　to　its　ground　level.　Numerical　simulations　show　that,　in　the　regime　of　strong　Kerr　nonlinearity　and　coupling　strengths,　the　protocol　can　produce　the　NOON　state　with　high　fidelity　in　the　cases　of　different　photon　numbers.　In　addition,　it　is　possible　for　the　protocol　to　produce　acceptable　fidelity　in　the　presence　of　systematic　errors　and　decoherence　factors.　Therefore,　the　protocol　may　provide　some　useful　perspectives　for　effective　generation　of　photonic　NOON　states.　©　2023　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement.