The team boss said that at Silverstone recently, the team was reassured that deciding to split with Renault is right.
Horner believes that moving to full works Honda power for 2019 is not too big a risk for the top F1 team.
"The situation is roughly similar between the two engines," he told France's Auto Hebdo, "but there is more room for development potential.
"Renault had a very difficult weekend at Silverstone," Horner added. "Our deficit was blatant, both in attack and defence.
"There is a gap to be filled and we have great confidence in Honda, especially given what they have in the pipeline.
"There is no guarantee, but the progress we have seen encourages us to believe that, little by little, we will get there."
The current championship continues this weekend with the German Grand Prix.