Update
With [bend right=70]
I need to adapt the nodes used at the end but the result is correct
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (n_3) at (1,1);
\coordinate (h_1) at (1.5,3);
\fill[blue] (n_3) circle (2pt);
\fill[blue] (h_1) circle (2pt);
\draw (n_3) to [bend right=70]
node[pos=0,sloped,minimum width=.8cm] (n_3) {}
node[pos=1,sloped,minimum width=.8cm] (h_1) {}
(h_1) ;
\draw (n_3.center) -- (n_3.west);
\draw (h_1.center) -- (h_1.west);
\end{tikzpicture}
\end{document}

Actually with shorten
and [bend right=70]
we get

In other cases, with simple curves, I prefer Jake's answer but my first try with shorten
was not efficient because I kept \documentclass{standalone}
so I searched another way.
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (n_3) at (1,1);
\coordinate (h_1) at (1.5,3);
\fill[blue] (n_3) circle (2pt);
\fill[blue] (h_1) circle (2pt);
\draw (n_3) to [bend right=5]
node[pos=0,sloped,minimum width=.8cm] (n_3) {}
node[pos=1,sloped,minimum width=.8cm] (h_1) {}
(h_1) ;
\draw (n_3.center) -- (n_3.west);
\draw (h_1.center) -- (h_1.east);
\end{tikzpicture}
\end{document}
