Finite element (FE) analysis of electrical machines with multiconductor windings can be computationally costly. This paper proposes a solution to this problem, using a reduced basis approach. The field-circuit problem is first solved in a single slot only with a set of different boundary conditions. These precomputed solutions are then used as shape functions to approximate the solution in all slots of the full problem. A polynomial interpolation method is also proposed for coupling the slot domains with the rest of the geometry, even if the geometries or meshes do not fully conform on the boundary. The method is evaluated on several test problems both in the frequency and time domains. According to the simulations, accurate solutions are obtained, 54-90 times faster as compared with the established FE approach.