Don't count backup slides

For the sake of completeness, here are two solutions inspired from the link given in my above comment.

1. You can define a new counter at the end of your presentation, before your backup slides, and use this counter at the end of your backup slides to fool beamer on the total number of slides. Here is a MWE:

   \documentclass{beamer}
   
   \usepackage{beamerthemesplit}
   \usepackage{lipsum}
   \usetheme{Madrid}
   
   \newcommand{\backupbegin}{
      \newcounter{finalframe}
      \setcounter{finalframe}{\value{framenumber}}
   }
   \newcommand{\backupend}{
      \setcounter{framenumber}{\value{finalframe}}
   }
   
   \begin{document}
   % Your normal slides go here 
   \frame{\lipsum[1]}
   \frame{\lipsum[2]}
   
   \appendix
   \backupbegin
   % And your backup slides here
   \frame{\lipsum[3]}
   \backupend
   
   \end{document}
   

   In this case, the backup slide is numbered as 3/2 in this example.

2. Alternatively, you can use the appendixnumberbeamer package. MWE:

   \documentclass{beamer}
   
   \usepackage{beamerthemesplit}
   \usepackage{lipsum}
   \usetheme{Madrid}
   \usepackage{appendixnumberbeamer}
   
   \begin{document}
   % Your normal slides go here 
   \frame{\lipsum[1]}
   \frame{\lipsum[2]}
   
   \appendix
   % And your backup slides here
   \frame{\lipsum[3]}
   
   \end{document}
   

   In this case, the backup slide is numbered as 1/1.

Old question and already lots of beamer-only solutions, but an alternate solution could be to build separatly the main presentation and the backup set of slides, and stitch the two pdf files together with pdftk. This way they are guaranteed to have separate numbering.

To keep formatting the same, you can put all the header stuff in a separate file, then just \input it in the two latex files.

For themes based on the infolines outer theme and a beamer version >= 3.49 you can use \setbeamertemplate{page number in head/foot}[appendixframenumber] after your theme to exclude the appendix from framenumbers displayed on the bottom of the frame.

\documentclass{beamer}
\usetheme{Madrid}

\setbeamertemplate{page number in head/foot}[appendixframenumber]

\begin{document}
\begin{frame}
  \frametitle{First slide}
\end{frame}

\appendix

\begin{frame}
content...
\end{frame}

\end{document}