In most of the carrier phase estimation (CPE) algorithms, there is a need to average a block of symbols to mitigate the noise effect. The symbols within a block may share the same derived phase (block estimation), or alternatively, a symbol by symbol sliding-window filter can be used to get each symbol a unique phase (sliding-window estimation). It is well-known that block estimation has lower estimation accuracy but consumes less computational power compared with sliding-window estimation. To improve the performance of CPE employing block estimation, we study and propose a phase interpolation filter that is simpler than the sliding-window filter, and show analytically that linear phase interpolation yields the best performance. Simulation and experimental results show that the phase interpolation filter effectively improves the performance of block estimation to the level similar to that of the sliding-window estimation.