Cecil got me thinking about writing exact expressions for the maximum
reactance for a given SWR, or equivalently for a given magnitude of
reflection coefficient. Barring clerical errors (and I've checked a
couple sample cases that seem OK), the following should be true.

Given r = magnitude of reflection coefficient in a system with a
real-valued reference impedance Z0, the maximum reactance will occur
when the reflection coefficient is

Rho = [2*r^2 + j*r*(1-r^2)]/(1+r^2)

Minimum reactance is obviously the complex conjugate of that.

The corresponding impedance is

Z = Z0 * (1+r^2 + j*2*r)/(1-r^2)

This may be commonly available in texts, or otherwise well known, but
I don't recall seeing it before, so thought I'd post it.

(Maximum and minimum resistance should be obvious)

Cheers,
Tom