Efforts to support the resolution of armed conflicts through the facilitation of peace negotiations and dialogues increasingly involve digital technologies. While traditionally perceived as a human-centered activity, peace mediation now commonly entails information- and data-driven methods to enhance talks, support the analysis of conflict stakeholder needs and interests, and ground mediation efforts in better evidence. Digital technologies also promise to make peace efforts more future-oriented by helping to predict or anticipate upcoming developments, build scenarios, and increase readiness for emerging challenges. However, little is known about how such methods can be employed in dialogue and negotiation settings, where participants may have subjective and incompatible views on the conflict context, and more data and evidence don’t necessarily help to determine what a more peaceful future could look like. Through a qualitative study of the use of digitally enhanced dialogue efforts in Yemen and Libya, we demonstrate that future-oriented peacemaking requires the balancing of ‘sincere’ technology affordances that encourage an engagement with the past and present reality of conflict, with ‘subjunctive’ technology affordances that encourage an engagement with possible futures that are more peaceful. In practice, this requires combining data- and evidence-generating methods concerned with the world ‘as is’ with data analysis and visualization methods concerned with how the world ‘should’ or ‘could’ be. Our findings have implications for the study of digital methods in the facilitation of contentious political processes where the provision of data and evidence may create hurting deadlocks.