The experimental heat transfer coefficients have been measured for two-phase convective boiling in two circular microtubes with inner diameters of $430{mu}m;and;792{mu}m$. While the heat transfer was greatly affected by the heat flux in the low quality region, the mass flux played a role in the high quality region. The smaller microtube had greater heat transfer coefficients. When the heat flux is varied from $20kW/m^2;to;30kW/m^2;at;G=240kg/m^2s$, the difference between the average heat transfer coefficients of the test tube $A(D_i=430{mu}m)$ and the test tube $B(D_i=792{mu}m)$ changes from $32.5\%;to;52.1\%$. At $G=370kg/m2^s$, the difference between the average heat transfer coefficients changes from $47.0\%;to;53.8\%$. A new correlation for the evaporative heat transfer coefficients in microtubes was developed by considering the following factors; the laminar flow heat transfer coefficient of liquid-phase flow, the enhancement factor of the convective heat transfer, and the nucleate boiling correction factor. The correlation developed in this study predicts the experimental heat transfer coefficients within an absolute average deviation of $8.4\%$.