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Quantum electrodynamics in very strong Coulomb fields is one scope which has not yet been tested experimentally with sufficient accuracy to really determine whether the perturbative approach is valid. One sensitive test is the determination of the 1s Lamb shift in highly-charged very heavy ions. The 1s Lamb shift of hydrogen-like lead (Pb 81+ ) and gold (Au 78+ ) has been determined using the novel detector concept of silicon microcalorimeters for the detection of hard x-rays. The results of  260 53 ( ) eV for lead and  211 42 () eV for gold are within the error bars in good agreement with theoretical predictions. To our knowledge, for hydrogen-like lead, this represents the most accurate determination of the 1s Lamb shift.