Achieving accurate measurements of inflammation levels in tissues or thickness changes in biological membranes (e.g., amniotic sac, parietal pleura) and thin biological walls (e.g., blood vessels) from outside the human body, is a promising research line in the medical area. It would provide a technical basis to study the options for early diagnosis of some serious diseases such as hypertension, atherosclerosis or tuberculosis. Nevertheless, achieving the aim of non-invasive measurement of those scarcely-accessible parameters on patient internal tissues, currently presents many difficulties. The use of high-frequency ultrasonic transducer systems appears to offer a possible solution. Previous studies using conventional ultrasonic imaging have shown this, but the spatial resolution was not sufficient so as to permit a thickness evaluation with clinical significance, which requires an accuracy of a few microns. In this paper a broadband ultrasonic technique, that was recently developed by the authors to address other non-invasive medical detection problems (by integrating a piezoelectric transducer into a spectral measuring system), is extended to our new objective; the aim is its application to the thickness measurement of sub-millimeter membranes or layers made of materials similar to some biological tissues (phantoms). The modeling and design rules of such a transducer system are described, and various methods of estimating overtones location in the power spectral density (PSD) are quantitatively assessed with transducer signals acquired using piezoelectric systems and also generated from a multi-echo model. Their effects on the potential resolution of the proposed thickness measuring tool, and their capability to provide accuracies around the micron are studied in detail. Comparisons are made with typical tools for extracting spatial parameters in laminar samples from echo-waveforms acquired with ultrasonic transducers. Results of this advanced measurement spectral tool are found to improve the performance of typical cross-correlation methods and provide reliable and high-resolution estimations.