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Nanoindentation refers to a class of experimental techniques where a micrometric force probe is used to quantify the local mechanical properties of soft biomaterials and cells. This approach has gained a central role in the fields of mechanobiology, biomaterials design and tissue engineering, to obtain a proper mechanical characterization of soft materials with a resolution comparable to the size of single cells (μm). The most popular strategy to acquire such experimental data is to employ an atomic force microscope (AFM); while this instrument offers an unprecedented resolution in force (down to pN) and space (sub-nm), its usability is often limited by its complexity that prevents routine measurements of integral indicators of mechanical properties, such as Young's Modulus (E). A new generation of nanoindenters, such as those based on optical fiber sensing technology, has recently gained popularity for its ease of integration while allowing to apply sub-nN forces with µm spatial resolution, therefore being suitable to probe local mechanical properties of hydrogels and cells. In this protocol, a step-by-step guide detailing the experimental procedure to acquire nanoindentation data on hydrogels and cells using a commercially available ferrule-top optical fiber sensing nanoindenter is presented. Whereas some steps are specific to the instrument used herein, the proposed protocol can be taken as a guide for other nanoindentation devices, granted some steps are adapted according to the manufacturer's guidelines. Further, a new open-source Python software equipped with a user-friendly graphical user interface for the analysis of nanoindentation data is presented, which allows for screening of incorrectly acquired curves, data filtering, computation of the contact point through different numerical procedures, the conventional computation of E, as well as a more advanced analysis particularly suited for single-cell nanoindentation data.