Here's one way to do it:
Define a new boolean citewithstar (which defaults to false).
Change the definition of the cite bibmacro so that a superscript star is added after the label number if citewithstar is true.
Define a macro \starnext that will set citewithstar to true for the next citation key.
Add \starnext in the prenote optional argument of the respectice citation command.
So far, there's one drawback: Adding \starnext in the prenote optional argument of the first/only citation key will produce an unwanted additional space. In this case, add \starnext before the citation command (see my example).
Note: You don't have to use "p.~13" in postnote optional arguments -- biblatex will assume that "13" is a page number and apply the correct formatting.
\documentclass{article}
\usepackage{biblatex}
\renewcommand*{\multicitedelim}{\addsemicolon\space}
\newbool{citewithstar}
\renewbibmacro*{cite}{%
\printtext[bibhyperref]{%
\printfield{prefixnumber}%
\printfield{labelnumber}%
\ifbool{citewithstar}{\textsuperscript{*}}{}% ADDED
\ifbool{bbx:subentry}
{\printfield{entrysetcount}}
{}}}
\newcommand*{\starnext}{%
\AtNextCitekey{\booltrue{citewithstar}}%
}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@MISC{Caesar,
author = {Caesar, Gaius J.},
title = {title},
year = {45BC},
}
@MISC{Cicero,
author = {Cicero, Marcus T.},
title = {title},
year = {44BC},
}
\end{filecontents*}
\addbibresource{\jobname.bib}
\begin{document}
\starnext\cites{Caesar}[13]{Cicero}
\cites{Caesar}[\starnext][13]{Cicero}
\printbibliography
\end{document}

If you'd like to specify the symbol in the label number suffix, a control sequence can take the place of citewithstar.
\documentclass{article}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style=numeric-comp,sorting=none]{biblatex}
\usepackage[colorlinks]{hyperref}
\renewcommand*{\multicitedelim}{\addsemicolon\space}
\DeclareFieldFormat{labelnumber}{\mkbiblabelsuffix{#1}}
\newrobustcmd*{\mkbibsuffix}[1]{%
\csgdef{cbx:suffix}{#1}}
\newrobustcmd*{\mkbiblabelsuffix}[1]{%
\ifcsundef{cbx:suffix}
{#1}
{#1\mkbibsuperscript{\csuse{cbx:suffix}}%
\global\csundef{cbx:suffix}}}
\addbibresource{biblatex-examples.bib}
\begin{document}
\mkbibsuffix{\dag}\cite[10--15]{companion}
\mkbibsuffix{*}\cites[10--15]{companion}[e.g.\mkbibsuffix{**}][]{ctan}{markey}{knuth:ct}
\mkbibsuffix{\ddag}\cites{companion}{ctan,markey,knuth:ct}
\printbibliography
\end{document}

\cite{Caesar}with and another citation of\cite{Caesar}without the star in the same document. – Martin Feb 26 '12 at 19:17