Correct reprogramming of epigenetic marks in the donor nuclei is a prerequisite for successful cloning by somatic cell transfer. In several mammalian species, repressive histone (H) lysine (K) trimethylation (me3) marks, in particular H3K9me3, form a major barrier to somatic cell reprogramming into pluripotency and totipotency. We engineered bovine embryonic fibroblasts for the doxycycline-inducible expression of Kdm4b, a demethylase that removes histone 3 lysine 9 trimethylation (H3K9me3) and H3K36me3 marks. Upon inducing Kdm4b, H3K9me3 and H3K36me3 levels reduced ∼3-fold and ∼5-fold, respectively, compared to non-induced controls. Donor cell quiescence has been previously associated with reduced somatic trimethylation levels and increased cloning efficiency in cattle. Simultaneously inducing Kdm4b expression (via doxycycline) and quiescence (via serum starvation), further reduced global H3K9me3 and H3K36me3 levels by a total of 18-fold and 35-fold, respectively, compared to non-induced, non-starved control fibroblasts. Following somatic cell transfer, Kdm4b-BEF fibroblasts reprogrammed significantly better into cloned blastocysts than non-induced donor cells. However, detrimethylated donors and sustained Kdm4b-induction during embryo culture did not increase rates of post-blastocyst development from implantation to survival into adulthood. In summary, KDM4B only improved somatic cell reprogramming into early preimplantation stages, highlighting the need for alternative experimental approaches to reliably improve somatic cloning efficiency in cattle.