A numerical simulation and various test-structure configurations were developed which enable the measurement of the in-plane thermal conductivity and emissivity of on-membrane thin films in a versatile and accurate manner. The simulation takes into account the two-dimensional heat transfer in the membrane. Consequently, shorter membrane can be used and strained materials can be measured. The numerical simulation along with the new test-structures is used to understand the convective heat transfer at small scales and to quantify it. The measurement method is tested on various materials ranging from ceramics, metals to polycrystalline silicon.