We employed the Very Large Array (VLA) of the National Radio Astronomy Observatory in C configuration to map 39 ultraluminous IRAS galaxies at 6~cm and 20~cm, at resolutions of ~ 4" and 15", respectively, and 24 sources at 6~cm with in the A configuration with a resolution of ~0.5". Most of the sources have radio spectral indices indicative of synchrotron emission (alpha ~ -0.65). There is one source, however, that shows an inverted spectrum with alpha = +2.1; observations at higher frequencies show that the spectrum peaks between 5 and 8 GHz, as high as any of the ``gigahertz peaked spectrum'' sources studied by O'Dea etal. We discuss the implications of this source for observations of fluctuations in the CMB. Two of the sources show multiple unresolved components, another four are doubles with at least one resolved component, 14 show extended emission which could arise from a disk, and two show arc-second long jets. Our data fit the tight correlation found by Helou etal (1985) between far-infrared and microwave luminosity; this correlation extends to the highest infrared luminosities. The correlation is weaker if only the extended or the nuclear components of the radio luminosity are used. Therefore the far-infrared emission in the majority of these higher luminosity galaxies is due to the same mechanism as the lower luminosity FIR sources, which is believed to be star formation, rather than non-thermal activity in the nucleus. Moreover, the star formation is not confined to the extended disk in these sources, but is important in the nucleus as well.