Not only must the coalition determine how its new philosophical approach might translate into practice, there are also fault-lines within the Government, and within the Conservative Party, which could ensure tensions over foreign policy, rather than quarrels about the economy, are the greatest threat to its survival.
Perhaps the most conspicuous source of disagreement between the Conservatives and their new partners remains Europe.
Liberal Democrats champion a central role for the UK within the EU. By contrast, the Tories' manifesto promised to repatriate powers from Brussels to London and Hague is on the eurosceptic wing.
The minister has a delicate balancing act to perform: maintaining constructive relationships with key EU countries, fending off excess Lib Dem euro-enthusiasm and, simultaneously, rampant euroscepticism in his own party.
David Cameron's instant rapport with Angela Merkel should help. Their views might diverge when it comes to EU integration, but at the latest G8 summit they formed a united front on deficit reduction.
Cameron's easy confidence on the world stage will aid the Foreign Minister as he juggles the coalition's conflicting views on Europe and strives to maintain a 'special relationship' with the US. But Hague could find differences with the Defence Secretary trickier.
Liam Fox is a proponent of the type of liberal interventionism practised by Blair and David Miliband.
In opposition, Fox scolded Russia during the war in South Ossetia and remained reluctant to revise his opinion after an EU investigation showed Georgia had started the conflict. It was an example of the type of grandstanding diplomacy which Hague has pledged to avoid.
Indeed, the Foreign Secretary specifically earmarked Russia, and a clutch of emerging world powers, like China, India and Brazil, as states with whom Britain should be seeking to develop closer partnerships.
He also suggested that the UK needs to look afresh at the size of our military. Fox has flatly rejected the notion that the Armed Forces could be reduced in size.
Nevertheless, in order to forge a balanced and successful foreign policy, Hague must ensure that his cautious approach prevails.
Likewise, he must find a middle way on Europe, avoiding the hard scepticism of the Tory right, as well as Lib Dem enthusiasm for an integrated EU which is badly out of step with voters.