This is a very wide question, answers to which range from period to nation to individual personalities.

In an attempt to answer a small portion of this, right at the beginning of your time period, we can look to the Field of Cloth of Gold in 1520 as a starting point. This was a historic moment between England and France, old wars and territory disputes briefly put to one side as the young kings Henry VIII and Francis I jointly hosted a meeting which lasted more than 2 weeks - today we would recognise it better as a festival. The best food, athletes and musical talents from both nations converged to create a spectacle, (somewhat) primary sources (Grafton) tell us that tents covered 10,000 square metres and their cloth was in fact woven with gold (hense the name). Both kings wanted to out do the other by demonstrating the prowess of their nations and the size of their retinue, but outwardly flattered each other - they entertained each others wives at dinners and we're told that one banquet was delayed because both kings insisted that the other was served first (I'm afriad I don't have the primary source for that to hand, but its listed in Antonia Fraser's book The Six Wives Of Henry VIII).

A second scenario is evidenced, again in the Tudor period, by Elizabeth I's attitude towards Mary Queen of Scots in the 1580s. Whilst Mary had been found guilty of plotting against Elizabeth, Elizabeth hesitated to sign the documents sanctioning her execution. Its widely believed that Elizabeth's concerns amounted to setting a precedent for executing an anointed monarch, who had the same claim to the divine right. Four months later, Elizabeth signed the warrant giving her consent to Mary's execution; however, when Mary was executed within days without prior agreement, Elizabeth was incandescent and claimed it had been done without her express permission.

Two very different interactions between very different monarchs.