More or less awkward (and more or less this trope) depending on the timeline. The "fairy tale" timeline strains their relationship the greatest, and they were never friends in the Mash parody line. The present-day and sci-fi timelines (especially down the road a few years) treat it as just a fact of their relationship - they both love Guinevere and each other too much to let it get in the way, and it's usually (usually) only a problem if someone else makes it a problem for them (like, say, political realities of their relationship or someone trying to reveal the queen is "unfaithful").
Elliot and Tedd in El Goonish Shive, driven home by the fact that, in an alternate universe where Elliot was born a girl, they're dating. Later revealed by Word of God to be true in nearly every alternate continuity where they are both alive and sexually compatible. Which is probably why Lord Tedd is such a grumpy gus - no Elliot and no relief (his "Grace" is an extremely large (and male) squirrel hybrid by the name of General Shade Tail).
MegaTokyo's Piro and Largo. Also, Kimiko and Erika. All are canonically straight, but the fact that each pair lives together, and have done so at least since college, doesn't help matters on the Ho Yay front.
Annie and Kat. (Again, The heterosexuality of this example is in dispute.)
Donald Donlan and James Eglamore are an example too. Surma even noted in one flashback that when Jim was away for training, Donnie seemed to miss Jim more than she did. Surma was Jim's girlfriend at the time.
Black and White from Grey is..., they live together and spend all their time together and care about each other more then anyone else
Terinu and Matt. They spent half their young lives together as the abused slaves as a pirate warlord, with Matt stealing food to keep Teri healthy and at one point he actually cuddled in bed with him after Terinu's powers were traumatically activated. Wordof God has stated "Both of them would rather be dead than see the other hurt."
Torg and Riff from Sluggy Freelance. Though even after being best friends for decades, they're still not that comfortable with hugs. Zoe and Gwynn too, for that matter.
Black Mage and Fighter from 8-Bit Theater. So...Fighter McWarrior and Blackmage Evilwizardington have been travelling together for probably years. No matter what made BM do that, it definitely qualifies them for the trope and if Fighter knew what heterosexual meant he'd probably describe their friendship like that. At least, FIGHTER would. Black Mage would stab Fighter a few dozen hundred times to illustrate his point as he said no. He would then probably Hadoken or evilstab the questioner. If Fighter's memory is to be trusted, they have been "best buds 4-eva" since when they were both kicked out of their respective schools, and continue to adventure together 3 years later in the epilogue.
Emergency Exit has quite a few relationships like this, the most obvious being the main characters and roommates Bob and Eddie as well as Karl and Jason even though Jason technically expressed romantic interest in Karl but since Karl's straight they are meerly very close friends.
Yu Han Sung: "Since Ro has left, I guess I should fire you, too. Since you two are a set menu, like a hamburger and a cola. It would be inhumane to separate the two of you. I hope you continue your beautiful love forever and ever."
Axel and Zexion in Ansem Retort. They're so close that Zexion was able to hit on Axel's wife-during their wedding-and not suffer a horrific death.
John and Dave, despite never meeting in person. The moirallegiance quadrant of the trolls' romance system combines this trope with elements of Morality Pet, though it's not restricted by gender at all and the most prominent examples are boy-girl.
The artist also stated that Shigeru and Taro are "bros for life", and it shows.
The main character 9 and his best friend, Chuckles, in Serious Emotional Disturbances. Lampshaded at one point during a reunion scene with a Celine Dion song being played as the two run towards each other. So much that the town of Bum*** (where they live), including 9's evil Gramma, assume the two are gay for each other.