I found a note on Microsoft SQL Azure (see Note 4.4) that stated that the hemisphere limitation is the same as Microsoft SQL Server 2008. That led to a blog post on how to calculate an envelope angle and several examples of supported/unsupported polygons.
Do I understand it well enough to reproduce here? Nope. However, there's a function, EnvelopeAngle that will calculate it.
The writer, Isaac Kunen, describes it as
"it is the maximum angle from the center to any of the points in the
figure, yielding a minimal cap with that center. The center, however,
is determined by summing the vectors from the center of the globe to
each vertex in the figure, essentially averaging the vertices."