We report the discovery and the results of follow-up timing observations of PSR J2045+3633 and PSR J2053+4650, two binary pulsars found in the Northern High Time Resolution Universe pulsar survey being carried out with the Effelsberg radio telescope. Having spin periods of 31.7 ms and 12.6 ms respectively, and both with massive white dwarf companions, $M_{c}, > , 0.8, M_{odot}$, the pulsars can be classified as mildly recycled. PSR J2045+3633 is remarkable due to its orbital period (32.3 days) and eccentricity $e, = , 0.01721244(5)$ which is among the largest ever measured for this class. After almost two years of timing the large eccentricity has allowed the measurement of the rate of advance of periastron at the 5-$sigma$ level, 0.0010(2)$^circ~rm yr^{-1}$. Combining this with a detection of the orthometric amplitude of the Shapiro delay, we obtained the following constraints on the component masses (within general relativity): $M_{p}, = , 1.33^{+0.30}_{-0.28}, M_{odot}$, and $M_{c}, = , 0.94^{+0.14}_{-0.13}, M_{odot}$. PSR J2053+4650 has a 2.45-day circular orbit inclined to the plane of the sky at an angle $i, = , 85.0^{+0.8}_{-0.9},{^circ}$. In this nearly edge-on case the masses can be obtained from the Shapiro delay alone. Our timing observations resulted in a significant detection of this effect giving: $M_{p}, = , 1.40^{+0.21}_{-0.18}, M_{odot}$, and $M_{c}, = , 0.86^{+0.07}_{-0.06}, M_{odot}$.
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