Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)
You could use the $p$-norm of the complex error $E(k)=Y_{data}(k)-Y_{syn}(k)$:

$$\epsilon_p=\sqrt[p]{\sum_{k=1}^K|E(k)|^p}\tag{1}$$

The most common values for $p$ are $p=2$ (Euclidean norm, $l_2$-norm) and $p=\infty$ (maximum norm or Chebyshev norm):

$$\epsilon_2=\sqrt{\sum_{k=1}^K|E(k)|^2}\tag{2}$$
$$\epsilon_{\infty}=\max_{1\le k\le K}\{|E(k)|\}\tag{3}$$

It eventually depends on your application which error measure best reflects the quality of the approximation. Note that for the maximum norm $(3)$, a single index $k$ determines the value of the error measure $\epsilon_{\infty}$, whereas the error measure $\epsilon_2$ in $(2)$ depends on all values of the complex error $E(k)$, and it is proportional to the square root of the mean squared error.