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Estimating the worst-case execution time (WCET) of real-time embedded systems is compulsory for the verification of their correct functioning. Traditionally, the WCET of a program is estimated assuming availability of the program's binary which is disassembled to reconstruct the program, and in some cases its source code to derive useful high-level execution information. However, in certain scenarios the program's owner requires that the binary of the program not be reverse-engineered to protect intellectual property, and in extreme situations, the program's binary is not available for the analysis, in which case it is substituted by program-execution traces. In this paper we show that we can obtain WCET estimates for programs based on runtime-generated or owner-provided time-stamped execution traces and without the need to access the source code or reverse-engineer the binaries of the programs. We show that we can provide very accurate WCET estimations using both integer linear programming (ILP) and constraint logic programming (CLP). Our method generates safe and tight WCET estimations for all the benchmarks used in the evaluation.