## 1 Introduction  
Metal corrosion has an economic and safety impact in several fields, such as automotive and oil industries and civil engineering [1]. In cultural heritage artifacts, corrosion products developed over centuries represent part of their history; consequently, they are generally preserved or partially removed. However, active corrosion phenomena can damage the objects, particularly those made of iron and copper alloys [2, 3, 4]. In this scenario, conservators implement protection and inhibition treatments and strategies to avoid further active degradation. For centuries, the application of protective coatings (e.g., resins, natural and synthetic waves, cellulose derivatives, or acrylic-based polymers) has been an effective method for this purpose [2, 3]. While not completely isolating the metallic surface [5], they can slow down the corrosion phenomena by reducing access to oxidizing agents and other pollutants [6]. A limited number of materials are suitable for application on metal-based cultural heritage objects because of the reversibility and stability characteristics required by conservation standards [2, 4, 7]. The effectiveness of protective coatings must be checked after their application and by constant monitoring throughout their lifespan, which can prompt coating substitution by conservators when signs of failure are detected (Figure 1) [8,9]. Several coating features may be monitored, including (a) chemical composition, (b) the application of the coating (particularly the thickness and homogeneity of the layer), (c) coating texture (i.e., porosity, roughness), and (d) electrochemical properties [8]. Different techniques have been tested to find suitable, easy, fast and non-destructive tools for conservators to constantly monitor the condition of a protective coating. This should preferably be performed at macro scale by mapping or by testing different areas of the object to determine the adequate time to remove and substitute the layers. Evaluation of the electrochemical properties, which generally requires direct contact between the probe and the object surface, is a relatively common approach in the metal conservation field because of its ease of use and portability. Eddy Currents (ECs) [10] allow for thickness estimation through sample conductivity (\(\sigma\)) measurement. This is performed by detecting the impedance variation induced by the secondary magnetic field produced by the sample as a result of the Eddy Currents [11,12]. Recently, innovative EC set-ups have been developed with more accurate thickness measurements, sometimes achieved through a contactless modality [13]. Electrochemical Impedance Spectroscopy (EIS), on the other hand, aids in inspecting protective coatings applied to different metallic objects by evaluating their barrier properties [2,4]. Despite the valuable complementary information provided, it might operate with limited lateral resolution, long acquisition times, and considerable uncertainty regarding the quantification of coating thickness [14]. In the last few decades, alternative systems to evaluate and monitor protective coatings have been tested. X-ray fluorescence spectroscopy (XRF) has been applied to measure and map the thickness of coating layers on silver artifacts [15,16]. The most recent advances in molecular spectroscopy, such as reflectance Fourier-transform infrared (rFTIR) and Near-infrared (NIR), have shown promising results for studying the chemical composition and evaluating the homogeneity of protective on bronze surfaces [17]. Other optical methods, such as Fiber Optic Reflectance Spectroscopy (FORS) [18], UV-induced visible fluorescence imaging [19], Fluorescence Lifetime Imaging (FLI) [20], ellipsometry [21] and  
Figure 1: Schematic representation of a cycle of evaluation and monitoring of a protective coating applied to a metallic surface in cultural heritage. Labels T0–T3 represent the different analytical campaigns required to monitor the coating performance through time.