Aligne side-by-side tables in LaTeX with float

The [t] after table has nothing to do with the alignment. It is a floating specifier which specifies the position a floating object can be placed on a page, e.g. the top of the page in case of [t].

If you want your table at a specific location, e.g. besides each other, don't put them in a floating environment like a table. Instead you can use the \captionof macro from the caption package.

To change the alignment, you can use the optional argument of the minipage to e.g. choose [t]op alignment.

Some other points:

• Your minipages have a combined width of 1\textwidth. If you want them side by side, you must remove the indention before them and protect your line endings with %, otherwise they will add an additional space

• the center environment adds additional vertical spacing. Use \centering instead

• by default the , in your numbers will result to incorrect spacing around it. If you want to use , as decimal separator, either use the icomma package or have a look at siunitx to properly format your numbers

\documentclass{article}

\usepackage{float}
\usepackage{caption}

\usepackage{geometry}
\usepackage{array}
\newcolumntype{C}[1]{p{#1}}
\usepackage{icomma}

\begin{document}

\noindent\begin{minipage}[t]{0.6\textwidth}%
              \centering
                \captionof{table}{Messwerte für Kalibrierung}
                \label{Tabelle 1}
                    \begin{tabular}{ |C{2cm} |C{2.3cm} |C{2.3cm}|}
                        \hline 
                         Kalibrations\-reihe & Transmission & Konzentration [in $\frac{mg}{L}$]
                        \\\hline
                        K1  & 0,059 & 1 \\
                        K2  & 0,323 & 5 \\
                        K3  & 0,648 & 10 \\
                        K4  & 0,96  & 15 \\ 
                        K5  & 1,211 & 20 \\ 
                        \hline
                    \end{tabular}
    \end{minipage}%
    \begin{minipage}[t]{0.4\textwidth}%
                \centering
                \captionof{table}{Probe und Referenz}
                \label{Tabelle 2}
                    \begin{tabular}{|c|c|}
                        \hline 
                        Probe & Transmission 
                        \\\hline
                        P1  & 1,032 \\
                        P2  & 1,037 \\\hline
                        R & 0,955 \\
                        \hline
                    \end{tabular}
    \end{minipage}%

\end{document}