The investment is the seventh completed by the Aberdeen-based private equity firm in the last nine months, and takes its total investment in oil services companies operating in the north east of Scotland to £30m.
Maven has installed a new managing director for the firm as part of the deal.
Bryan Fagan, who joined in March, was part of the management team who sold Dominion Gas to Praxair.
He is also a former sales director for Phoenix Polymers.
RMEC, which employs 22 staff and turns over £9m, said company founders and majority shareholders Alan Ramsay and Stuart Mathers will remain part of the management team to help implement its growth strategy.
The business, which has an enterprise value of £14m, aims to position itself as a leader in the manufacture, maintenance, repair, testing, recertification and rental of well services equipment.
The founders have not netted windfalls as part of the buy-in.
Mr Fagan said the company will use the investment to boost staff numbers, expand workshop and storage capacity in Forfar, and increase its fleet of rental equipment for clients operating in the North Sea.
While he said it was too early to declare how many jobs will be created, he confirmed the company was looking to add to its management team in the areas of finance and operations.
Noting that RMEC has no immediate plans to offer its services beyond the UK Continental Shelf, Mr Fagan said the Maven investment is the "kick-start that we needed to grow the business in the North Sea as much as we have in our plans".
He said: "With an excellent workforce, established customer base, enviable long-term contracts, first-class testing and storage facilities and well-equipped workshop in acres of land south of Aberdeen, RMEC has a strong platform on which to build.
"This capital injection will fast-track our aim of becoming a major player in well services, offering a competitive solution with a best in class, personalised service."
Ewan MacKinnon, investment director at Maven Capital Partners, said the private equity firm's latest investment comes as the appetite among investors for energy services companies is "very strong ".
Asked if Maven was likely to conclude further deals in oil and gas services sector, he said: "I would hope so, it's in the sweet spot that we like. It's a really nice business; it's grown very well over the last few years.
"The economy is still pretty buoyant up here so, absolutely, I would hope we would see more deals like this."
Mr MacKinnon noted a key attraction of RMEC as an investment was the relative resilience of its business model. He added: "Even if something was to happen to oil prices it is a pretty resilient sector, given that you have to get certification done.
"Integrity is very, very key in the North Sea at the minute, and those are things that we at Maven like as an investment.
"It's a really nice sub-sector of the oil and gas sector."
Mr MacKinnon added that demand for services provided by companies such as RMEC will continue despite resources being limited in the North Sea.
He noted: "The North Sea is declining, there is less oil. That's a fact. But if you've got an ageing infrastructure offshore, it means there is more maintenance required, there's more certification required. For a business like this that's not a bad thing.
"The oil is reducing, but you need to keep the assets around the North Sea going, therefore for the likes of an RMEC that's excellent news."
Mr MacKinnon said Maven investors, who typically make their investments via venture capital trusts, tend to remain with a business for three to six years. However, he noted Maven was not "time-constrained" in terms of when it ultimately exits a company.
Nick Dalgarno of Simmons and Company International, who advised Mr Ramsay and Mr Mathers on the deal, said: "This is an excellent deal for the founders and the new investors which realises the value of the current business and sets the company up for significant future growth."