Near-field radiative heat transfer (NFRHT) between planar metallic surfaces was computationally explored over five decades ago by Polder and van Hove [Phys. Rev. B 4, 3303 (1971)PLRBAQ0556-280510.1103/PhysRevB.4.3303]. These studies predicted that, as the gap size (d) between the surfaces decreased, the radiative heat flux first increases by several orders of magnitude until d is ∼100 nm after which the heat flux saturates. However, despite both the fundamental and practical importance of these predictions, the combined enhancement and saturation of NFRHT at small gaps in metallic surfaces remains experimentally unverified. Here, we probe NFRHT between planar metallic (Pt, Au) surfaces and show that RHT rates can exceed the far-field rate by over a thousand times when d is reduced to ∼25 nm. More importantly, we show that for small values of d RHT saturates due to the dominant contributions from transverse electric evanescent modes. Our results are in excellent agreement with the predictions of fluctuational electrodynamics and are expected to inform the development of technologies such as near-field thermophotovoltaics, radiative heat-assisted magnetic recording, and nanolithography.