This thesis concerns case-marking phenomena in Icelandic and Faroese. I argue that the best approach to case distinguishes the levels of abstract, morphosyntactic and morphological case, and permits mismatches between levels in some grammars (Linking Theory, Kiparsky 1997, 2001); these mismatches are best handled by an Optimality Theoretic output harmonisation on the mapping from argument structure to morphosyntax (Prince and Smolensky 1993 et seq.). Such a theory provides a cogent account of predicates with non-nominative subjects in Insular Scandinavian, which present an interesting puzzle: in Icelandic, dative-subject verbs occur with nominative objects that trigger number agreement, whereas in Faroese the object in such sentences is marked accusative and occurs with default third person singular agreement. To date this difference has been poorly understood, and calls for in-depth analysis. The central hypothesis explored in this thesis is that the patterns observed are not language-specific idiosyncrasies, but the outcome of constraint interactions of a typical kind: namely, a pressure to index a nominative argument in the clause by number agreement, and a pressure to express structural accusative case on the object. I argue that similar constraint conflicts are responsible for the loss of lexical case in phenomena such as nominative substitution and case non-preservation, and correctly predict the availability of the passive in dative-subject predicates. I include a substantial amount of new data from surveys conducted on the Faroe Islands and Iceland, which are consistent with my hypothesis, and shed new light on the case systems of these languages beyond simple monotransitives. Moreover, I propose a Competing Grammars Model of intra-linguistic variation (cf. Kroch 1989 et seq.), which finds empirical support in corpora, and offers a plausible framework for explaining the diachronic trajectory of these languages. Finally, the model of grammar proposed here is also cross-linguistically tractable, generating realistic typologies of case-related phenomena, and can easily be extended to other language families.