We show that capillary waves can exist at the boundary between miscible coflowing fluids. We unveil that the interplay between transient interfacial stresses and confinement drives the progressive transition from the well-known inertial regime, characterized by a frequency independent wave number, k∼ω^{0}, to a capillary wave scaling, k∼ω^{2/3}, unexpected for miscible fluids. This allows us to measure the effective interfacial tension between miscible fluids and its rapid decay on timescales never probed so far, which we rationalize with a model going beyond square-gradient theories. Our work potentially opens a new avenue to measure transient interfacial tensions at the millisecond scale in a controlled manner.