Mobile phones continuously monitor and evaluate indicators of the received signal strengths from surrounding base stations to optimise wireless services. These signal strength indicators (SSIs) offer the potential for assessing radiofrequency electromagnetic field (RF-EMF) exposure on a population scale, as they can be related to exposure from both base stations and handset devices. Within the ETAIN (Exposure To electromAgnetic fields and plaNetary health) project, an open-access RF-EMF exposure app for smartphones, named "5G Scientist Monitor”, has been developed using citizen science. This paper delineates a measurement protocol for deriving formulas to convert the app SSIs into electric field values to estimate RF-EMF exposure. It presents pilot study results from measurements taken at four locations in Lyon, France (FR), and 14 locations in the Netherlands (NL), using three different phone models and the most common network providers in each country. The measurements were conducted while executing different usage scenarios, such as calls or data transmission. The exposimeter ExpoM-RF4 and on-body electric field probes were used to measure exposure from far-field sources and the handset, respectively. Two-minute aggregates were considered the sample unit for analyses (n=891 in NL and n=395 in FR). Regression analyses showed a positive log-linear relationship between Long Term Evolution (LTE) SSIs and far-field RF-EMF exposure when aggregating data by location (coefficients for the normalised RSSI: 0.91 [95% CI: 0.55 - 1.28] in FR, 1.09 [95% CI: 0.96 - 1.22] in NL). Negative log-linear trends were observed for handset-related RF-EMF exposure at the ear (-0.31 [95% CI: -0.46 - -0.16]) and chest (-0.20 [95% CI: -0.37 - -0.03]) during data transmission scenarios. These results demonstrate that the 5G-Scientist-Monitor app can be implemented for smartphone-based RF-EMF estimation. However, uncertainties in individual measurement points highlight the need for further data collection and analysis to improve the accuracy of exposure estimates.