For the bibliography
\renewcommand*{\@biblabel}[1]{[\romannumeral 0#1]}
should work (of course within \makeatletter...\makeatother).
Without hyperref you could use
\renewcommand\citeform[1]{\romannumeral 0#1}
for the citations as suggested in the cite manual. Unfortunately, hyperref turns the argument of \citeform into an unexpandable link, so the formatting can't be applied at this late stage. With hyperref interfering I could get things to work by redefining \bibcite.
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{cite}
\usepackage{filecontents}
\usepackage{hyperref}
\makeatletter
\def\bibcite#1#2{%
\@newl@bel{b}{#1\@extra@binfo}{%
\hyper@@link[cite]{}{cite.#1\@extra@b@citeb}{\romannumeral 0#2}%
}%
}
\renewcommand*{\@biblabel}[1]{[\romannumeral 0#1]}
\makeatother
\begin{filecontents}{\jobname.bib}
@Article{art1,
author = {Author, A. N.},
title = {Title One},
journal = {Journal},
year = 2000
}
@Article{art2,
author = {Author, A. N.},
title = {Title Two},
journal = {Journal},
year = 2008
}
\end{filecontents}
\begin{document}
Refering to second article\cite{art2} and then first article\cite{art1}
\bibliographystyle{unsrt}
\bibliography{\jobname}
\end{document}
As the eagle-eyed will have spotted the margin is off because the margin width calculation is done on the BibTeX side assuming arabic numerals.

The llncs.cls class you use redefines \@biblabel directly in its definition of thebibliography, we can only counter this by redefining the entire environment
\makeatletter
\renewenvironment{thebibliography}[1]
{\section*{\refname}
\renewcommand*{\@biblabel}[1]{[\romannumeral 0##1]}%
\small
\list{\@biblabel{\@arabic\c@enumiv}}%
{\settowidth\labelwidth{\@biblabel{#1}}%
\leftmargin\labelwidth
\advance\leftmargin\labelsep
\if@openbib
\advance\leftmargin\bibindent
\itemindent -\bibindent
\listparindent \itemindent
\parsep \z@
\fi
\usecounter{enumiv}%
\let\p@enumiv\@empty
\renewcommand\theenumiv{\@arabic\c@enumiv}}%
\if@openbib
\renewcommand\newblock{\par}%
\else
\renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
\fi
\sloppy\clubpenalty4000\widowpenalty4000%
\sfcode`\.=\@m}
{\def\@noitemerr
{\@latex@warning{Empty `thebibliography' environment}}%
\endlist}
\makeatother
splncs_src.bst[https://github.com/tvcutsem/es-lab/blob/master/doc/esop13/splncs_srt.bst] withllncs. May be, that is causing the problem. – hola Sep 27 '18 at 16:07llncs.cls? This should be caused by the document class and not by the.bstfile? – moewe Sep 27 '18 at 16:09llncs.clsfrom https://www.springer.com/de/it-informatik/lncs/conference-proceedings-guidelines – moewe Sep 27 '18 at 16:16hyperref, use\renewcommand*{\@biblabel}[1]{[\romannumeral 0#1]}AND\renewcommand\citeform[1]{\romannumeral 0#1}. If you use hyperref, look at the complete code. – Gqqnbig Feb 28 '22 at 13:11