Depending on the species, males have different strategies to try and insure that they reproduce, rather than just being a step-parent.

They may try to ensure paternity by increased surveillance and fighting off the competition, they may have more frequent sex with their long-term partners, they may physically punish unfaithful females or refuse to parent potentially unrelated offspring.

Reed warblers (Acrocephalus scirpaceus)
 are socially monogamous, defend their territory, and both parents care for the offspring. Scientists recently tried to experimentally test the behavior of reed warblers after a potential act of "cheating" by the female. How does the male treat a competitor, and how does an "affair" affect care for the brood? To answer these questions they simulated an increased risk of adulterous behavior in female reed warblers by briefly introducing a caged extra male to 31 reed warbler pairs during the female´s fertile period. In addition they played back recorded songs of randomly selected warbler males from the area. The scientists then observed nest building activity and feeding of offspring, and determined chick paternity through DNA analyses.

 They found that the males aggressively try to chase off competitors and to keep potentially "double-dealing" females in line. But whether or not they manage, they turn out to be caring fathers once the babies are born.

From previous observations it was known that male territory owners will aggressively try to chase away intruders (conspecific males) as soon as they detect them. This territorial behavior is interpreted as a paternity guard. They observed that all males tried to attack and chase away the caged intruder. When the female appeared to show interest in the intruder, the male behaved considerably more aggressively, both to the intruder and to his female partner. Almost half of the females did not even approach the newcomer. 

First author Herbert Hoi explains, "We think that the males are more aggressive when their partners are watching because first, it only pays for the male to show off when the "babe" is watching him, and second, he certainly has more reason to fear being cuckolded or even losing his partner when the newcomer approaches his female." 

They found that many nests housed nestlings fathered outside the pair-bond. This was the case both in the experimental and in the control group. Those females that had been observed to show interest in the intruder were also later found to be more likely to have extra-pair chicks in their nest. In addition, the results suggest that larger females seem to be more promiscuous.

Extra-pair paternity in relation to the presence of an intruder. Proportion of nests with or without extra-pair young (upper graph) and average proportion of extra-pair nestlings (lower graph) in relation to the occurrence of an intruder during the fertile period. Link and credit: 
doi:10.1371/journal.pone.0062541

Cuckolded males are caring fathers

The researchers then looked at whether offspring care was affected by paternity uncertainty. The results were surprising: Males seem to readily procure food for the chicks, regardless whether they are their own or not. Females, however, cared significantly less for their young if they had been faced with the simulated intruder. Perhaps the female´s potential infidelity had no effect on the male´s subsequent feeding investment because he cannot distinguish his own from an extra-pair chick.

On the other hand, females who perceived their males as unable to repel an intruder quickly enough and therefore as a "weakling", then invest less in the joint offspring. The only chance a male has to ensure successful paternity seems to be to quickly get rid of potential competitors.

Citation: Hoi H, Krištofík J, Darolová A (2013) Experimentally Simulating Paternity Uncertainty: Immediate and Long-Term Responses of Male and Female Reed Warblers Acrocephalus scirpaceus. PLoS ONE 8(4): e62541. doi:10.1371/journal.pone.0062541