Recent work by Matui–Sato has shown that certain classes of C*-algebras with a unique trace (eg. UHF algebras) also give rise to ultrapowers with a unique trace. Winters asked if, more generally, every trace on an ultrapower is necessarily a limit of traces on the original (separable) algebra. We show that this fails quite generally for C*-algebras with ’large enough’ trace space. We also show how you can even get a trace ’coming out of nowhere’, i.e. an element (xn) of the ultrapower of A on which a trace is non-zero even though t(xn) = 0 for every trace t on A. This is a joint work with Ilijas Farah.