Here I show it 5 times. 1st example shows the \left...\right problem, example 2 shows the fix for that from Stretchable delimiters ignoring overline.
The current problem is shown in example 3, with a \vphantom fix given in example 4 and the \myoverline fix in example 5,as referenced in Overline thickness, and modified to take an optional real number for the overline offset.
\documentclass{book}
\usepackage{stackengine}
\usepackage{scalerel}
\parskip 1ex \relax
\parindent 0pt\relax
\newcommand\noverline[1]{\vphantom{#1}\smash{\overline{#1}}}
\newcommand\myoverline[2][1.2]{\ThisStyle{%
\setbox0=\hbox{$\SavedStyle#2$}%
\stackengine{#1\LMpt}{$\SavedStyle#2$}{\rule{\wd0}{.4\LMpt}}{O}{c}{F}{F}{S}%
}}
\begin{document}
Original, with problem:\\
$\left\{ f \right\} \; \left\{ \overline{f} \right\}$
Referenced \verb|\noverline|:\\
$\left\{ f \right\} \; \left\{ \noverline{f} \right\}$
problem in current question:\\
$\noverline{\left\{ f \right\} \; \left\{ \noverline{f} \right\}}$
Vphantom superscript:\\
$\noverline{\left\{ f \right\}^{\vphantom{x}} \; \left\{ \noverline{f} \right\}}$
With \verb|\myoverline| and \verb|\noverline|:\\
$\myoverline[1.9]{\left\{ f \right\} \; \left\{ \noverline{f} \right\}}$
\end{document}

The net result is that we can now dispense with \overline and replace the reference to it in \noverline with \myoverline, so that \noverline can now take the optional argument of \myoverline (and works across math styles).
\documentclass{book}
\usepackage{stackengine}
\usepackage{scalerel}
\newcommand\noverline[2][1.2]{\vphantom{#2}\smash{\myoverline[#1]{#2}}}
\newcommand\myoverline[2][1.2]{\ThisStyle{%
\setbox0=\hbox{$\SavedStyle#2$}%
\stackengine{#1\LMpt}{$\SavedStyle#2$}{\rule{\wd0}{.4\LMpt}}{O}{c}{F}{F}{S}%
}}
\begin{document}
$\noverline[1.9]{\left\{ f \right\} \; \left\{ \noverline{f} \right\}}$
$\scriptscriptstyle\noverline[1.9]{\left\{ f \right\} \; \left\{ \noverline{f} \right\}}$
\end{document}

Note: If one wants the smaller math style overline to remain as thick as in display style (which is the case for the original \overline), then one need merely change the .4\LMpt length to .4pt, in the definition of \myoverline.
\vphantomexponent, as in$\noverline{\left\{ f \right\}^{\vphantom{x}} \; \left\{ \noverline{f} \right\}}$. Change thexto something else to affect the offset. – Steven B. Segletes Jul 07 '16 at 15:15stackengineapproach, such as\myoverlineat http://tex.stackexchange.com/questions/167954/overline-thickness/167995#167995 allows offsets to be specified, and may help you in this case. – Steven B. Segletes Jul 07 '16 at 15:22