  We study the problem of estimating the $ST$-diameter of a graph that is
subject to a bounded number of edge failures. An $f$-edge fault-tolerant
$ST$-diameter oracle ($f$-FDO-$ST$) is a data structure that preprocesses a
given graph $G$, two sets of vertices $S,T$, and positive integer $f$. When
queried with a set $F$ of at most $f$ edges, the oracle returns an estimate
$\widehat{D}$ of the $ST$-diameter $\operatorname{diam}(G-F,S,T)$, the maximum
distance between vertices in $S$ and $T$ in $G-F$. The oracle has stretch
$\sigma \geq 1$ if $\operatorname{diam}(G-F,S,T) \leq \widehat{D} \leq \sigma
\operatorname{diam}(G-F,S,T)$. If $S$ and $T$ both contain all vertices, the
data structure is called an $f$-edge fault-tolerant diameter oracle ($f$-FDO).
An $f$-edge fault-tolerant distance sensitivity oracles ($f$-DSO) estimates the
pairwise graph distances under up to $f$ failures.
  We design new $f$-FDOs and $f$-FDO-$ST$s by reducing their construction to
that of all-pairs and single-source $f$-DSOs. We obtain several new tradeoffs
between the size of the data structure, stretch guarantee, query and
preprocessing times for diameter oracles by combining our black-box reductions
with known results from the literature.
  We also provide an information-theoretic lower bound on the space requirement
of approximate $f$-FDOs. We show that there exists a family of graphs for which
any $f$-FDO with sensitivity $f \ge 2$ and stretch less than $5/3$ requires
$\Omega(n^{3/2})$ bits of space, regardless of the query time.
