No-insulation and partial-insulation are novel approaches for compact, high field rare-earth-Ba2Cu3O7-x-coated conductor magnets. They maximize the current density and overcome some of the coated conductors' intrinsic challenges such as the low normal zone propagation velocity and the resulting difficulties to quench REBCO magnets safely. However, this comes at a reduction of the field quality and an increase of the charging time. The performance of this type of coils is mainly determined by the contact resistance between the different layers of the winding. In the case of partially-insulated coils, the contact resistance can be adjusted by a tailored choice of the material used for the metal co-winding or for the metallic coating of the REBCO tape. We present here a systematic study of the impact of pressure on the contact resistance in the cases of direct contact (no-insulation) as well as metal co-winding and metal coating (partial-insulation). Different “insulation” metals as well as various “insulation” to REBCO tape ratios are tested at 77 K in self-field varying the contact pressure in the range of 10–200 MPa. The goal is to provide coil manufacturers with the means of achieving a controlled contact resistance to optimize the coil performance.