  In passive fluid-fluid phase separation, a single interfacial tension sets
both the capillary fluctuations of the interface and the rate of Ostwald
ripening. We show that these phenomena are governed by two different tensions
in active systems, and compute the capillary tension $\sigma_{cw}$ which sets
the relaxation rate of interfacial fluctuations in accordance with capillary
wave theory. We discover that strong enough activity can cause negative
$\sigma_{cw}$. In this regime, depending on the global composition, the system
self-organizes, either into a microphase-separated state in which coalescence
is highly inhibited, or into an `active foam' state. Our results are obtained
for Active Model B+, a minimal continuum model which, although generic, admits
significant analytical progress.
