run somebody close
run someone a close second
run a close second

(This rail line parallels and runs very close to the existing Route 7.)

New rules designed to "manage competition" had created a dangerous situation in which cars ran too close together without the horsepower to surge out of harm's way.

"The broad lines of the party platforms run very close to each other," the respected daily El Pais said in an editorial.

It must be hard to do, because normally they are able to run teasingly close but always just out of reach of the pursuing men.

The three cars continued to run very close together.

They were running quite close together and behind them galloped the judge and other men.

Unfortunately the allocated course ran very close to where Königin Luise had laid her mines.

The route of the Pennine Way footpath runs very close to the buildings.

Yes - it certainly seemed as if the stream ran very close to the house indeed.

Some of them ran so close past Tarzan that he could almost have reached out and touched them.