Now, the top team Red Bull is jumping aboard, and top official Dr Helmut Marko thinks Red Bull-Honda is on track for a world championship tilt.
Verstappen said Red Bull is buzzing with "positive energy", thanks to the new works partnership with Honda.
"We'll have to wait and see". They are making good progress.
Max had a forgetful first half of the season, one where he was heavily criticised for crashing multiple times and not keeping a steady head during tight situations.
"It will all depend on what the others have done, but certainly versus themselves there has been good progress".
In November, the Austrian team ended an 11-year partnership with Renault, whose engines powered them to four successive driver and constructor title doubles between 2010 and 2013.
But although there are no guarantees about the durability of the Honda power unit that it will start the season with, Horner says he would not be too upset if his team was forced to take extra power units in 2019.
"I think his maturity has increased, we saw that during the course of previous year".
"It's a huge challenge to do the season on three engines", he said. "We would rather see consistent evolution, even if that means taking a penalty or two along the way. So long as the progress and trajectory is on the right way, there's a lot of optimism within the team, within the factory, and excitement about working in collaboration with a new partner".
Team boss Horner is quoted by Speed Week: "Honda is having a strong winter".
"It is a very different scenario", he said.
"This is the first time that Red Bull and Honda have collaborated, and we know that at the beginning of a relationship, it always takes a little time for things to become automatic and you get the most out of it. We're extremely hopeful the performance will be a step from where we've been the last few years".