Recent U-Pb dating by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) has demonstrated that reasonable precision (3 %-10 %, 2span classCombining double low line"inline-formula"/i/span) can be achieved for high-resolution dating of texturally distinct calcite phases. Absolute dating of dolomite, for which biostratigraphy and traditional dating techniques are very limited, remains challenging, although it may resolve many fundamental questions related to the timing of mineral-rock formation by syngenetic, diagenesis, hydrothermal, and epigenetic processes. In this study we explore the possibility of dating dolomitic rocks via recent LA-ICP-MS dating techniques developed for calcite. The in situ U-Pb dating was tested on a range of dolomitic rocks of various origins from the Cambrian to Pliocene age - all of which are from well-constrained stratigraphic sections in Israel. We present imaging and chemical characterization techniques that provide useful information on interpreting the resulting U-Pb ages and discuss the complexity of in situ dolomite dating in terms of textural features that may affect the results. Textural examinations indicate zonation and mixing of different phases at the sub-millimeter scale (span classCombining double low line"inline-formula"</span 1 span classCombining double low line"inline-formula"μ/spanm), and thus Tera-Wasserburg ages represent mixed dates of early diagenesis and some later epigenetic dolomitization event(s). We conclude that age mixing at the sub-millimeter scale is a major challenge in dolomite dating that needs to be further studied and note the importance of matrix-matched standards for reducing uncertainties of the dated material.