Aims. PSR J1846−0258 is a young rotation-powered pulsar with one of the highest surface magnetic field strengths, located in the centre of SN-remnant Kes-75. In June 2006 a magnetar-like outburst took place. Using multi-year RXTE and INTEGRAL observations covering the epoch of the outburst, we aim to study the temporal and spectral characteristics of PSR J1846−0258 over a broad ∼3-300 keV energy range to derive constraints on theoretical scenarios aiming to explain this schizophrenic behaviour. Methods. We explored all publically available RXTE observations of PSR J1846−0258 to generate accurate ephemerides over the period January 30, 2000-November 7, 2007. Phase-folding procedures yielded pulse profiles for RXTE PCA (∼3-30 keV), RXTE HEXTE (∼15-250 keV) and INTEGRAL ISGRI (∼20-300 keV). The pulsed spectrum over the full ∼3-300 keV energy range was derived, as well as the total spectrum (including the pulsar wind nebula) over the 20-300 keV band with the ISGRI. The timing, spatial, and spectral analyses were applied for epochs before, during, and after the magnetar-like outburst to study the evolution of the high-energy characteristics. Results. ISGRI detected PSR J1846−0258/Kes-75 before outburst during 2003-2006 with a power-law-shape spectrum over the 20-300 keV energy range with photon index Γ = 1.80 ± 0.06 and energy flux (20-300 keV) of (6.62 ± 0.35) × 10 −11 erg/cm 2 s. More than 90 days after the onset of the outburst, still during the decay phase, the same spectral shape was measured (Γ = 1.75 +0.27 −0.31 ) with an indication for a 52% (2.3σ) enhanced total emission, while one year after the outburst the hard X-ray non-thermal emission of PSR J1846−0258/Kes-75 was found to be back to its pre-outburst values. PCA monitoring of PSR J1846−0258 before the outburst yielded phase-coherent ephemerides confirming the earlier derived breaking index of the spindown. During the outburst, incoherent solutions have been derived. We show that the radiative outburst was triggered by a major spin-up glitch near MJD 53 883 ± 3 with a glitch size Δν/ν in the range (2.0−4.4) × 10 −6 . Using all pre-outburst observations of ISGRI and HEXTE for the first time pulse profiles have been obtained up to 150 keV with a broad single asymmetric pulse. The pulse shape did not vary with energy over the 2.9-150 keV energy range, nor did it change during the magnetar-like outburst. The time-averaged pre-outburst ∼3-300 keV pulsed spectrum measured with the PCA, HEXTE, and ISGRI was fitted with a power-law model with Γ = 1.20 ± 0.01. A fit with a curved power-law model gives an improved fit. Around 150 keV the pulsed fraction approaches 100%. For the first 32 days of the magnetarlike outburst, the 3-30 keV pulsed spectrum can be represented with two power laws, a soft component with index Γ s = 2.96 ± 0.06 and a hard component with the pre-outburst value Γ h ∼ 1.2. Above ∼9 keV, all spectra during outburst are consistent with the latter single power-law shape with index ∼1.2. The 2-10 keV flux increased by a factor ∼5 and the 10...