Artificial electromagnetic surfaces, metasurfaces, control light in the desired manner through the introduction of abrupt changes of electromagnetic fields at interfaces. Current modelling of metasurfaces successfully exploits generalised sheet transition conditions (GSTCs), a set of boundary conditions that account for electric and magnetic metasurface-induced optical responses. GSTCs are powerful theoretical tools but they are not readily applicable for arbitrarily shaped metasurfaces. Accurate and computationally efficient algorithms capable of implementing artificial boundary conditions are highly desired for designing free-form photonic devices. To address this challenge, we propose a numerical method based on conformal boundary optics with a modified finite difference time-domain (FDTD) approach which accurately calculates the electromagnetic fields across conformal metasurfaces. Illustrative examples of curved meta-optics are presented, showing results in good agreement with theoretical predictions. This method can become a powerful tool for designing and predicting optical functionalities of conformal metasurfaces for new lightweight, flexible and wearable photonic devices.