High pressure resistivity measurements of the organic compound (TMTTF)2BF4 have been performed in a newly developped Bridgman cell providing good pressure conditions on a wide pressure range. For the first time in this compound a zero resistance superconducting state is observed between 3 and 4GPa. At temperatures above the superconducting transition, the resistivities of the two high quality samples show a different behavior. One sample, provides indications for a magnetic quantum critical point at the maximum of Tc, whereas in the other antiferromagnetic spin-fluctuations are present above Tc.