The pendant drop apparatus is used in order to study the surface tension of ethene-1-butene random copolymer melts over the whole range of compositions, including poly(1-butene) (P-1-B) and at different temperatures. Furthermore, the surface tensions of isotactic polypropene (i-PP) and syndiotactic polypropene (s-PP) are measured. The surface tension of the melt of random copolymers decreases as a function of copolymer composition from pure polyethene (PE) to pure P-1-B in a nearly exponential manner, and the surface tensions of copolymers with a P-1-B content in the range of approximately 40 wt % match the surface tension of i-PP and s-PP. This indicates the possible existence of a window of miscibility. This result is verified by the calculation of the solubility parameters from additional sessile drop measurements on solid copolymers at room temperature and from pressure-volume-temperature data of the melts applying the Flory-Orwoll-Vrij equation-of-state theory. Also, the theory of the conformational parameter beta (Bates and Fredrickson) leads to the same conclusion. All results are consistent with microscopic observations discussed in the literature.