The hosts came out of the blocks quicker in the battle between Peninsula Premier East and West, with Steve Bowker seeing his early shot saved by visiting keeper Brodie Cole.
Jordan Frost then guided his header just over from a corner, before Brad Frost came the closest of anyone on 20 minutes when he thumped a fierce volley against the crossbar with Cole rooted to his line.
Both sides then struggled to seize the initiative as the half went on, with a succession of niggly fouls disrupting the rhythm.
Callington’s first decent sight of goal came moments before the break, but Ben Clark could only fire wide after an impressive run through midfield.
Clark would keep home stopper Paul Thompson busy with a couple of efforts in the second period as the visitors found their feet – as would the lively Steve Edwards.
But ultimately the goals would live a charmed life as the two Step Six sides came away with 90 more minutes in the legs.
And as far as Darts joint manager Gary Lobb was concerned, the game provided a good workout for his players.
‘We played a friendly the other day against a team from Plymouth and we beat them about 20-0,’ he explained.
‘The lads got 90 minutes in their legs but this was a much more difficult game today, much more of a battle and playing against a much better, more experienced team.
‘We encountered different ideas today, and as far as I’m concerned it was a great 90 minutes of preparation.’
Like many teams in the area, Dartmouth have been affected by a rise in Covid cases across the South West.
‘Our pre-season has been hit quite hard by Covid,’ Lobb said. ‘We’ve had two or three games called off and this week has been a bit up and down.
‘The referee cried off on Tuesday afternoon, and trying to get another one has been a nightmare, really.
‘Covid is taking its toll on everything. Like others we have been suffering from a lack of players due to them having to self isolate.
‘But we have to work with it, move forward and just keep doing what we can.’
Callington manager Matt Hayden was keen to take the positives from what he saw as a scrappy encounter.
‘You do pre-season now to get minutes in the tank and get the boys to enjoy themselves,’ Hayden said.
‘It was scrappy from the start. We lost a couple of players early on so organisationally it became a little bit disjointed.
‘I changed things a bit after that and then we got ourselves properly into the game. We started settling down and taking full control.
‘To come to here, have a scrappy game and have it finish 0-0 with a clean sheet – I think that is a positive.’
And he added: ‘We’ve played teams that are a bit lower than us and we’ve done really well against them. We’ve come up here against a team at the same level and they are a good side.
‘They have a very good system of play, they work hard, they battle for each other. It’s another learning curve. Every game we’ve had is another learning curve.
‘The game against [midweek opponents] Tiverton was a massive one for us in terms of shape, discipline and everything like that. This was about how we could manage the game.
‘Against a team who work hard and battle, can we manage the game so that we don’t come away with a defeat? We got the draw and in the league that’s a point. You can’t argue with that.’
Dartmouth’s next friendly will see them welcome Devon Football League side Teignmouth to Longcross on Wednesday, July 21 (7.30pm). Callington, meanwhile, make the trip to face The Windmill on the same evening (7.30pm).