We present optical and near-infrared observations of two Type Ibn supernovae (SNe), SN 2018jmt and SN 2019cj. Their light curves have rise times of about 10 days, reaching an absolute peak magnitude of Mg(SN 2018jmt)=-19.07+/-0.37 and MV(SN 2019cj)=-18.94+/-0.19mag, respectively. The early-time spectra of SN 2018jmt are dominated by a blue continuum, accompanied by narrow (600-1000km/s) HeI lines with P-Cygni profile. At later epochs, the spectra become more similar to those of the prototypical SN Ibn 2006jc. At early phases, the spectra of SN 2019cj show flash ionisation emission lines of CIII, NIII and HeII superposed on a blue continuum. These features disappear after a few days, and then the spectra of SN 2019cj evolve similarly to those of SN 2018jmt. The spectra indicate that the two SNe exploded within a He-rich circumstellar medium (CSM) lost by the progenitors a short time before the explosion. We model the light curves of the two SNe Ibn to constrain the progenitor and the explosion parameters. The ejecta masses are consistent with either that expected for a canonical SN Ib (~2M_{sun}) or those from a massive WR star (>~4M{sun}), with the kinetic energy on the order of 1051 erg. The lower limit on the ejecta mass (>~2M{sun}) argues against a scenario involving a relatively low-mass progenitor (e.g., MZAMS~10M{sun}). We set a conservative upper limit of ~0.1M{sun}_ for the 56Ni masses in both SNe. From the light curve modelling, we determine a two-zone CSM distribution, with an inner, flat CSM component, and an outer CSM with a steeper density profile. The physical properties of SN 2018jmt and SN 2019cj are consistent with those expected from the core collapse of relatively massive, stripped-envelope (SE) stars.