The Ginzburg‐Landau equations are solved for thin superconductors in the presence of arbitrary tangential magnetic fields and yield an essentially position‐independent order parameter if the superconductor contains no vortices. The magnetic transition is always first order unless the field is symmetrical on the surface; if the field comes from a superposition of external source and transport current, the critical order parameter &PHgr;cis a one‐third power function of the current. It is shown that the physical conditions for the above solution can be realized with a superconducting transmission line, and that the order parameter is directly measurable in terms of the resonant frequency of the line. The measurements made on tin samples at temperatures down to 0.6Tcshow excellent agreement with the theory, and constitute an experimental vertification of the latter.