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This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a)\u00a0a hierarchical error bound<\/jats:italic> and (b)\u00a0an error bound based on an auxiliary linear problem<\/jats:italic>, to the case of port-Hamiltonian systems. The approaches rely on a secondary approximation of (a) the dynamical system and (b) the error system. In this paper, these methods are adapted to port-Hamiltonian systems. The mathematical relationship between the two methods is discussed both theoretically and numerically. The effectiveness of the described methods is demonstrated using a challenging three-dimensional port-Hamiltonian model of a classical guitar with fluid\u2013structure interaction.<\/jats:p>","DOI":"10.1007\/s10444-024-10195-8","type":"journal-article","created":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T06:02:27Z","timestamp":1726034547000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improved a posteriori error bounds for reduced port-Hamiltonian systems"],"prefix":"10.1007","volume":"50","author":[{"given":"Johannes","family":"Rettberg","sequence":"first","affiliation":[]},{"given":"Dominik","family":"Wittwar","sequence":"additional","affiliation":[]},{"given":"Patrick","family":"Buchfink","sequence":"additional","affiliation":[]},{"given":"Robin","family":"Herkert","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0003-2850-1440","authenticated-orcid":false,"given":"J\u00f6rg","family":"Fehr","sequence":"additional","affiliation":[]},{"given":"Bernard","family":"Haasdonk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"10195_CR1","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1017\/S0962492922000083","volume":"32","author":"V Mehrmann","year":"2023","unstructured":"Mehrmann, V., Unger, B.: Control of port-Hamiltonian differential-algebraic systems and applications. 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