Phase difference between electric and magnetic fields of EM wave in a conductor?
In equation 9.133 of Griffiths it is stated that
$$\phi = \tan^{-1}\frac{\kappa}{k}$$
where (according to equation 9.125):

\$\phi\$ is the phase angle between the electric and magnetic fields,
\$\kappa\$ is the imaginary part of the complex wave-number
\$k\$ is the real part of the complex wave-number

According to Equation 9.126, one should have.
$$(\frac{\kappa}{k})^2 = \frac{\sqrt{1+\frac{\sigma}{\epsilon\omega}}-1}{\sqrt{1+\frac{\sigma}{\epsilon\omega}}+1}$$
And,
$$\lim_{\sigma \rightarrow \infty}\frac{\sqrt{1+\frac{\sigma}{\epsilon\omega}}-1}{\sqrt{1+\frac{\sigma}{\epsilon\omega}}+1} = 1$$
So, when conductivity \$\sigma\$ is very high, \$\phi\$ tends to 45 degrees.