High resolution spectral models for simple stellar populations (SSP) developed in the past few years have become a standard ingredient in studies of stellar population of galaxies. As more such models become available, it becomes increasingly important to test them. In this and a companion paper, we test a suite of publicly available evolutionary synthesis models using integrated optical spectra in the blue-near-UV range of 27 well studied star clusters from the work of Leonardi & Rose (2003) spanning a wide range of ages and metallicities. Most (23) of the clusters are from the Magellanic clouds. This paper concentrates on methodological aspects of spectral fitting. The data are fitted with SSP spectral models from Vazdekis and collaborators, based on the MILES library. Best-fit and Bayesian estimates of age, metallicity and extinction are presented, and degeneracies between these parameters are mapped. We find that these models can match the observed spectra very well in most cases, with small formal uncertainties in t, Z and A_V. In some cases, the spectral fits indicate that the models lack a blue old population, probably associated with the horizontal branch. This methodology, which is mostly based on the publicly available code STARLIGHT, is extended to other sets of models in Paper II, where a comparison with properties derived from spatially resolved data (color-magnitude diagrams) is presented. The global aim of these two papers is to provide guidance to users of evolutionary synthesis models and empirical feedback to model makers.
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