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We present the results of a search for high-redshift (z > 9) galaxy candidates in the JWST UNCOVER survey, using deep NIRCam and NIRISS imaging in seven bands over ∼45 arcmin2 and ancillary Hubble Space Telescope (HST) observations. The NIRCam observations reach a 5σ limiting magnitude of ∼29.2 AB. The identification of high-z candidates relies on a combination of a dropout selection and photometric redshifts. We find 16 candidates at 9 < z < 12 and three candidates at 12 < z < 13, eight candidates are deemed very robust. Their lensing amplification ranges from μ = 1.2 to 11.5. Candidates have a wide range of (lensing corrected) luminosities and young ages, with low stellar masses [6.8 < log(M⋆/M⊙) < 9.5] and low star formation rates (SFR = 0.2–7 M⊙ yr−1), confirming previous findings in early JWST observations of z > 9. A few galaxies at z ∼ 9−10 appear to show a clear Balmer break between the F356W and F444W/F410M bands, which helps constrain their stellar mass. We estimate blue UV continuum slopes between β = −1.8 and −2.3, typical for early galaxies at z > 9 but not as extreme as the bluest recently discovered sources. We also find evidence for a rapid redshift-evolution of the mass-luminosity relation and a redshift evolution of the UV continuum slope for a given range of intrinsic magnitude, in line with theoretical predictions. These findings suggest that deeper JWST observations are needed to reach the fainter galaxy population at those early epochs, and follow-up spectroscopy will help better constrain the physical properties and star formation histories of a larger sample of galaxies.